Find the value of $\int\int\frac{1}{16x^2+16x+10} \,dx$.

$(x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$

$\frac{1}{8} (x+\frac{1}{2})Sin^{-1} (x+\frac{1}{2})-\frac{1}{2} ln⁡(1+(x+\frac{1}{2})^2)$

$\frac{1}{8} (x+\frac{1}{2})tan^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$

$(x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$

$\frac{1}{8} (x+\frac{1}{2}) sec^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$

Find the value of $\int\int_0^y \frac{2xy^5}{\sqrt{1+x^2 y^2-y^4}} dxdy$.

$2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$

$2[\frac{y^4}{4}- \frac{2}{3} (1-y^4)^{\frac{3}{2}}]$

$2[\frac{y^4}{4}- (1-y^4)^{\frac{3}{2}}]$

$2[\frac{y^4}{4}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$

$2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$

Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy.

(–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))

(x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(y3 Cos(y) + 3[y2 Sin(y) – 2[-yCos(y) + Sin(y)]])

(-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3[y2 Sin(y) – 2[-yCos(y) + Sin(y)]])

(-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y))

(–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))

Find the value of ∫∫ x⁄x2 + y2 dxdy.

[ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]

x [ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]

y [xtan(-1) (x)- 1⁄2 ln⁡(1+x2)]

x [ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]

FIND_THE_AREA_INSIDE_FUNCTION_(2X3_+_5_X2_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_4)‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´X2_FROM_X_=_1_TO_A?$#

a2‚Äö√Ñ√∂‚àö√ñ‚àö√´2 + 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 11‚Äö√Ñ√∂‚àö√ñ‚àö√´2

a2‚Äö√Ñ√∂‚àö√ñ‚àö√´2 + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® 4ln(a)

a2‚Äö√Ñ√∂‚àö√ñ‚àö√´2 + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 11‚Äö√Ñ√∂‚àö√ñ‚àö√´2

a2‚Äö√Ñ√∂‚àö√ñ‚àö√´2 + 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 11‚Äö√Ñ√∂‚àö√ñ‚àö√´2

a2‚Äö√Ñ√∂‚àö√ñ‚àö√´2 + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® 11‚Äö√Ñ√∂‚àö√ñ‚àö√´2

Find the integration of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•0x x2 + y2 dxdy$

x4‚Äö√Ñ√∂‚àö√ñ‚àö√´6

2x3‚Äö√Ñ√∂‚àö√ñ‚àö√´3y

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xy7 Cos(x)Cos(y) dxdy$

(7y6 Cos(y) + 42y5 Sin(y) + 210y4 Cos(y) + 840y3 Sin(y) + 2520y2 Cos(y) + 5040ySin(y) + 5040Cos(y))(7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x))

(y7 Sin(y) + 7y6 Cos(y) + 42y5 Sin(y) + 210y4 Cos(y) + 840y3 Sin(y) + 2520y2 Cos(y) + 5040ySin(y) + 5040Cos(y))(x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x))

(y7 Sin(y) + 42y5 Sin(y) + 210y4 Cos(y) + 840y3 Sin(y) + 2520y2 Cos(y) + 5040ySin(y) + 5040Cos(y))(x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x))

(y7 Sin(y) + 7y6 Cos(y) + 42y5 Sin(y) + 210y4 Cos(y) + 840y3 Sin(y) + 2520y2 Cos(y) + 5040ySin(y) + 5040Cos(y))(x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x))

Find the ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•x3 y3 sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(x)sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(y) dxdy$

(‚Äö√Ñ√∂‚àö√ë‚àö¬®x3 Cos(x) + 6xCos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(x))(-y3 Cos(y))

(x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(y3 Cos(y) + 3[y2 Sin(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 2[-yCos(y) + Sin(y)]])

(-x3 Cos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 3x2 Sin(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3[y2 Sin(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 2[-yCos(y) + Sin(y)]])

(-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(y))

(‚Äö√Ñ√∂‚àö√ë‚àö¬®x3 Cos(x) + 6xCos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(x))(-y3 Cos(y))

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬• x‚Äö√Ñ√∂‚àö√ñ‚àö√´x2 + y2 dxdy$

[ytan(-1) (y)- 1‚Äö√Ñ√∂‚àö√ñ‚àö√´2 ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y2 )].

x [ytan(-1) (y)- 1‚Äö√Ñ√∂‚àö√ñ‚àö√´2 ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y2 )].

y [xtan(-1) (x)- 1‚Äö√Ñ√∂‚àö√ñ‚àö√´2 ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+x2 )].

x [ytan(-1) (y)- 1‚Äö√Ñ√∂‚àö√ñ‚àö√´2 ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y2 )].

14 + Mcqs in Double Integrals in Engineering Mathematics Page 1 McqOptions

1.	Find the value of $\int\int\frac{1}{16x^2+16x+10} \,dx$.
A.	$\frac{1}{8} (x+\frac{1}{2})Sin^{-1} (x+\frac{1}{2})-\frac{1}{2} ln⁡(1+(x+\frac{1}{2})^2)$
B.	$\frac{1}{8} (x+\frac{1}{2})tan^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$
C.	$(x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$
D.	$\frac{1}{8} (x+\frac{1}{2}) sec^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$
Answer» C. $(x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)$

Discussion

2.	Find the value of $\int\int_0^{1-y} xy\sqrt{1-x-y} \,dxdy$.
A.	16⁄946
B.	8⁄945
C.	16⁄936
D.	16⁄945
Answer» E.

Discussion

3.	Find the value of $\int\int_0^y \frac{2xy^5}{\sqrt{1+x^2 y^2-y^4}} dxdy$.
A.	$2[\frac{y^4}{4}- \frac{2}{3} (1-y^4)^{\frac{3}{2}}]$
B.	$2[\frac{y^4}{4}- (1-y^4)^{\frac{3}{2}}]$
C.	$2[\frac{y^4}{4}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$
D.	$2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$
Answer» D. $2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]$

Discussion

4.	Find the integration of ∫∫0x x2 + y2 dxdy.
A.	x4⁄6
B.	y
C.	2x3⁄3y
D.	1
Answer» D. 1

Discussion

5.	Find the integration of $\int\int_0^{\sqrt{2ax-x^2}}x \,dxdx$.
A.	ax2⁄2 – x5⁄30
B.	ax2⁄2 – x3⁄6
C.	ax2⁄2
D.	ax4⁄8 – x3⁄6
Answer» C. ax2⁄2

Discussion

6.	Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy.
A.	(x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(y3 Cos(y) + 3[y2 Sin(y) – 2[-yCos(y) + Sin(y)]])
B.	(-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3[y2 Sin(y) – 2[-yCos(y) + Sin(y)]])
C.	(-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y))
D.	(–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))
Answer» D. (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))

Discussion

7.	Find the value of ∫∫ x⁄x2 + y2 dxdy.
A.	[ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]
B.	x [ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]
C.	y [xtan(-1) (x)- 1⁄2 ln⁡(1+x2)]
D.	x [ytan(-1) (y)- 1⁄2 ln⁡(1+y2)]
Answer» E.

Discussion

8.	Find the value of ∫∫xyex + y dxdy.
A.	yey (xex-ex)
B.	(yey-ey)(xex-ex)
C.	(yey-ey)xex
D.	(yey-ey)(xex+ex)
Answer» C. (yey-ey)xex

Discussion

9.	FIND_THE_AREA_INSIDE_FUNCTION_^{(2X³_+_5_X²_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_4)}‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´_X²_FROM_X_=_1_TO_A?$#
A.	<sup>a<sup>2</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® 4ln(a)
B.	<sup>a<sup>2</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® <sup>11</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>
C.	<sup>a<sup>2</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> + 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® <sup>11</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>
D.	<sup>a<sup>2</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> + 5a ‚Äö√Ñ√∂‚àö√ë‚àö¬® <sup>11</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>
Answer» C. <sup>a<sup>2</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> + 4ln(a) ‚Äö√Ñ√∂‚àö√ë‚àö¬® <sup>11</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub>

Discussion

10.	Find the integration of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•₀^x x² + y² dxdy$
A.	<sup>x<sup>4</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>6</sub>
B.	y
C.	<sup>2x<sup>3</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>3</sub>y
D.	1
Answer» D. 1

Discussion

11.	Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xy⁷ Cos(x)Cos(y) dxdy$
A.	(7y<sup>6</sup> Cos(y) + 42y<sup>5</sup> Sin(y) + 210y<sup>4</sup> Cos(y) + 840y<sup>3</sup> Sin(y) + 2520y<sup>2</sup> Cos(y) + 5040ySin(y) + 5040Cos(y))(7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x))
B.	(y<sup>7</sup> Sin(y) + 7y<sup>6</sup> Cos(y) + 42y<sup>5</sup> Sin(y) + 210y<sup>4</sup> Cos(y) + 840y<sup>3</sup> Sin(y) + 2520y<sup>2</sup> Cos(y) + 5040ySin(y) + 5040Cos(y))(x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x))
C.	(y<sup>7</sup> Sin(y) + 42y<sup>5</sup> Sin(y) + 210y<sup>4</sup> Cos(y) + 840y<sup>3</sup> Sin(y) + 2520y<sup>2</sup> Cos(y) + 5040ySin(y) + 5040Cos(y))(x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x))
D.	(y<sup>7</sup> Sin(y) + 7y<sup>6</sup> Cos(y) + 42y<sup>5</sup> Sin(y) + 210y<sup>4</sup> Cos(y) + 840y<sup>3</sup> Sin(y) + 2520y<sup>2</sup> Cos(y) + 5040ySin(y) + 5040Cos(y))(x<sup>7</sup> Sin(x) + 7x<sup>6</sup> Cos(x) + 42x<sup>5</sup> Sin(x) + 210x<sup>4</sup> Cos(x) + 840x<sup>3</sup> Sin(x) + 2520x<sup>2</sup> Cos(x) + 5040xSin(x) + 5040Cos(x))
Answer» E.

Discussion

12.	Find the ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•x³ y³ sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(x)sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(y) dxdy$
A.	(x<sup>3</sup> Cos(x) + 3x<sup>2</sup> Sin(x) + 6xCos(x)-6Sin(x))(y<sup>3</sup> Cos(y) + 3[y<sup>2</sup> Sin(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 2[-yCos(y) + Sin(y)]])
B.	(-x<sup>3</sup> Cos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 3x<sup>2</sup> Sin(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6xCos(x)-6Sin(x))(-y<sup>3</sup> Cos(y) + 3[y<sup>2</sup> Sin(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 2[-yCos(y) + Sin(y)]])
C.	(-x<sup>3</sup> Cos(x) + 3x<sup>2</sup> Sin(x) + 6xCos(x)-6Sin(x))(-y<sup>3</sup> Cos(y) + 3y<sup>2</sup> Sin(y) + 6yCos(y) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(y))
D.	(‚Äö√Ñ√∂‚àö√ë‚àö¬®x<sup>3</sup> Cos(x) + 6xCos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(x))(-y<sup>3</sup> Cos(y))
Answer» D. (‚Äö√Ñ√∂‚àö√ë‚àö¬®x<sup>3</sup> Cos(x) + 6xCos(x) ‚Äö√Ñ√∂‚àö√ë‚àö¬® 6Sin(x))(-y<sup>3</sup> Cos(y))

Discussion

13.	Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬• ^x‚Äö√Ñ√∂‚àö√ñ‚àö√´_{x² + y²} dxdy$
A.	[ytan<sup>(-1)</sup> (y)- <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y<sup>2</sup> )].
B.	x [ytan<sup>(-1)</sup> (y)- <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y<sup>2</sup> )].
C.	y [xtan<sup>(-1)</sup> (x)- <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+x<sup>2</sup> )].
D.	x [ytan<sup>(-1)</sup> (y)- <sup>1</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>2</sub> ln‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(1+y<sup>2</sup> )].
Answer» E.

Discussion

14.	Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xye^{x + y} dxdy
A.	ye<sup>y</sup> (xe<sup>x</sup>-e<sup>x</sup> )
B.	(ye<sup>y</sup>-e<sup>y</sup>)(xe<sup>x</sup>-e<sup>x</sup>)
C.	(ye<sup>y</sup>-e<sup>y</sup> )xe<sup>x</sup>
D.	(ye<sup>y</sup>-e<sup>y</sup> )(xe<sup>x</sup>+e<sup>x</sup> )
Answer» C. (ye<sup>y</sup>-e<sup>y</sup> )xe<sup>x</sup>

Discussion

1.	Find the value of \(\int\int\frac{1}{16x^2+16x+10} \,dx\).
A.	\(\frac{1}{8} (x+\frac{1}{2})Sin^{-1} (x+\frac{1}{2})-\frac{1}{2} ln⁡(1+(x+\frac{1}{2})^2)\)
B.	\(\frac{1}{8} (x+\frac{1}{2})tan^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)\)
C.	\((x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)\)
D.	\(\frac{1}{8} (x+\frac{1}{2}) sec^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)\)
Answer» C. \((x+1/2) cos^{-1} (x+\frac{1}{2})-\frac{1}{16} ln⁡(1+(x+\frac{1}{2})^2)\)

3.	Find the value of \(\int\int_0^y \frac{2xy^5}{\sqrt{1+x^2 y^2-y^4}} dxdy\).
A.	\(2[\frac{y^4}{4}- \frac{2}{3} (1-y^4)^{\frac{3}{2}}]\)
B.	\(2[\frac{y^4}{4}- (1-y^4)^{\frac{3}{2}}]\)
C.	\(2[\frac{y^4}{4}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]\)
D.	\(2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]\)
Answer» D. \(2[\frac{y^3}{3}-\frac{2}{3} (1-y^4)^{\frac{3}{2}}]\)

Explore topic-wise MCQs in Engineering Mathematics.

Find the value of \(\int\int\frac{1}{16x^2+16x+10} \,dx\).

Find the value of \(\int\int_0^{1-y} xy\sqrt{1-x-y} \,dxdy\).

Find the value of \(\int\int_0^y \frac{2xy^5}{\sqrt{1+x^2 y^2-y^4}} dxdy\).

Find the integration of ∫∫0x x2 + y2 dxdy.

Find the integration of \(\int\int_0^{\sqrt{2ax-x^2}}x \,dxdx\).

Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy.

Find the value of ∫∫ x⁄x2 + y2 dxdy.

Find the value of ∫∫xyex + y dxdy.

FIND_THE_AREA_INSIDE_FUNCTION_^{(2X³_+_5_X²_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_4)}‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´_X²_FROM_X_=_1_TO_A?$#

Find the integration of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•₀^x x² + y² dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xy⁷ Cos(x)Cos(y) dxdy$

Find the ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•x³ y³ sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(x)sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(y) dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬• ^x‚Äö√Ñ√∂‚àö√ñ‚àö√´_{x² + y²} dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xye^{x + y} dxdy

Explore topic-wise MCQs in Engineering Mathematics.

Find the value of \(\int\int\frac{1}{16x^2+16x+10} \,dx\).

Find the value of \(\int\int_0^{1-y} xy\sqrt{1-x-y} \,dxdy\).

Find the value of \(\int\int_0^y \frac{2xy^5}{\sqrt{1+x^2 y^2-y^4}} dxdy\).

Find the integration of ∫∫0x x2 + y2 dxdy.

Find the integration of \(\int\int_0^{\sqrt{2ax-x^2}}x \,dxdx\).

Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy.

Find the value of ∫∫ x⁄x2 + y2 dxdy.

Find the value of ∫∫xyex + y dxdy.

FIND_THE_AREA_INSIDE_FUNCTION_(2X3_+_5_X2_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_4)‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´X2_FROM_X_=_1_TO_A?$#

Find the integration of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•0x x2 + y2 dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xy7 Cos(x)Cos(y) dxdy$

Find the ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•x3 y3 sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(x)sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(y) dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬• x‚Äö√Ñ√∂‚àö√ñ‚àö√´x2 + y2 dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xyex + y dxdy

FIND_THE_AREA_INSIDE_FUNCTION_^{(2X³_+_5_X²_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_4)}‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´_X²_FROM_X_=_1_TO_A?$#

Find the integration of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•₀^x x² + y² dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xy⁷ Cos(x)Cos(y) dxdy$

Find the ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•x³ y³ sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(x)sin‚Äö√Ñ√∂‚àö√ñ¬¨‚àû(y) dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬• ^x‚Äö√Ñ√∂‚àö√ñ‚àö√´_{x² + y²} dxdy$

Find the value of ‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•‚Äö√Ñ√∂‚àö‚Ä†¬¨¬•xye^{x + y} dxdy