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 u2061(1+(x+ frac{1}{2})^2) )

( frac{1}{8} (x+ frac{1}{2})Sin^{-1} (x+ frac{1}{2})- frac{1}{2} ln u2061(1+(x+ frac{1}{2})^2) )

( frac{1}{8} (x+ frac{1}{2})tan^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )

((x+1/2) cos^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )

( frac{1}{8} (x+ frac{1}{2}) sec^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(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 value of 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 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 u2061(1+y2)]

x [ytan(-1) (y)- 1 2 ln u2061(1+y2)]

y [xtan(-1) (x)- 1 2 ln u2061(1+x2)]

x [ytan(-1) (y)- 1 2 ln u2061(1+y2)]

10 + 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 u2061(1+(x+ frac{1}{2})^2) )
B.	( frac{1}{8} (x+ frac{1}{2})tan^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )
C.	((x+1/2) cos^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )
D.	( frac{1}{8} (x+ frac{1}{2}) sec^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )
Answer» C. ((x+1/2) cos^{-1} (x+ frac{1}{2})- frac{1}{16} ln u2061(1+(x+ frac{1}{2})^2) )

Discussion

2.	Find the area inside function ^{(2x³ + 5 x² 4)} _x² from x = 1 to a.
A.	<sup>a<sup>2</sup></sup> <sub>2</sub> + 5a 4ln(a)
B.	<sup>a<sup>2</sup></sup> <sub>2</sub> + 5a 4ln(a) <sup>11</sup> <sub>2</sub>
C.	<sup>a<sup>2</sup></sup> <sub>2</sub> + 4ln(a) <sup>11</sup> <sub>2</sub>
D.	<sup>a<sup>2</sup></sup> <sub>2</sub> + 5a <sup>11</sup> <sub>2</sub>
Answer» C. <sup>a<sup>2</sup></sup> <sub>2</sub> + 4ln(a) <sup>11</sup> <sub>2</sub>

Discussion

3.	Find the value of ( int int_0^{1-y} xy sqrt{1-x-y} ,dxdy ).
A.	<sup>16</sup> <sub>946</sub>
B.	<sup>8</sup> <sub>945</sub>
C.	<sup>16</sup> <sub>936</sub>
D.	<sup>16</sup> <sub>945</sub>
Answer» E.

Discussion

4.	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

5.	Find the integration of ₀^x x² + y² dxdy.
A.	<sup>x<sup>4</sup></sup> <sub>6</sub>
B.	y
C.	<sup>2x<sup>3</sup></sup> <sub>3</sub>y
D.	1
Answer» D. 1

Discussion

6.	Find the value of 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

7.	Find the integration of ( int int_0^{ sqrt{2ax-x^2}}x ,dxdx ).
A.	<sup>ax<sup>2</sup></sup> <sub>2</sub> <sup>x<sup>5</sup></sup> <sub>30</sub>
B.	<sup>ax<sup>2</sup></sup> <sub>2</sub> <sup>x<sup>3</sup></sup> <sub>6</sub>
C.	<sup>ax<sup>2</sup></sup> <sub>2</sub>
D.	<sup>ax<sup>4</sup></sup> <sub>8</sub> <sup>x<sup>3</sup></sup> <sub>6</sub>
Answer» C. <sup>ax<sup>2</sup></sup> <sub>2</sub>

Discussion

8.	Find the x³ y³ sin (x)sin (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) 2[-yCos(y) + Sin(y)]])
B.	(-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) 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) 6Sin(y))
D.	( x<sup>3</sup> Cos(x) + 6xCos(x) 6Sin(x))(-y<sup>3</sup> Cos(y))
Answer» D. ( x<sup>3</sup> Cos(x) + 6xCos(x) 6Sin(x))(-y<sup>3</sup> Cos(y))

Discussion

9.	Find the value of ^x _{x² + y²} dxdy.
A.	[ytan<sup>(-1)</sup> (y)- <sup>1</sup> <sub>2</sub> ln u2061(1+y<sup>2</sup>)]
B.	x [ytan<sup>(-1)</sup> (y)- <sup>1</sup> <sub>2</sub> ln u2061(1+y<sup>2</sup>)]
C.	y [xtan<sup>(-1)</sup> (x)- <sup>1</sup> <sub>2</sub> ln u2061(1+x<sup>2</sup>)]
D.	x [ytan<sup>(-1)</sup> (y)- <sup>1</sup> <sub>2</sub> ln u2061(1+y<sup>2</sup>)]
Answer» E.

Discussion

10.	Find the value of 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

Explore topic-wise MCQs in Engineering Mathematics.

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

Find the area inside function (2x3 + 5 x2 4) x2 from x = 1 to a.

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 value of xy7 Cos(x)Cos(y) 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 4)} _x² from x = 1 to a.

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

Find the value of xy⁷ Cos(x)Cos(y) dxdy.

Find the x³ y³ sin (x)sin (y) dxdy.

Find the value of ^x _{x² + y²} dxdy.

Find the value of xye^{x + y} dxdy.