What is $\smallint \frac{{{\rm{dx}}}}{{{{\rm{a}}^2}{{\sin }^2}{\rm{x}} + {{\rm{b}}^2}{{\cos }^2}{\rm{x}}}}$ equal to?Where c is the constant of integration.

Question

What is $\smallint \frac{{{\rm{dx}}}}{{{{\rm{a}}^2}{{\sin }^2}{\rm{x}} + {{\rm{b}}^2}{{\cos }^2}{\rm{x}}}}$ equal to?Where c is the constant of integration.

TuteeHUB · Accepted Answer

${\rm{c}} - \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{b}}\tan {\rm{x}}}}{{\rm{b}}}} \right)$

TuteeHUB · Answer

${\rm{c}} + \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{a}}\tan {\rm{x}}}}{{\rm{b}}}} \right)$

TuteeHUB · Answer

${\rm{c}} + \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{b}}\tan {\rm{x}}}}{{\rm{a}}}} \right)$

TuteeHUB · Answer

None of the above

1.	What is \(\smallint \frac{{{\rm{dx}}}}{{{{\rm{a}}^2}{{\sin }^2}{\rm{x}} + {{\rm{b}}^2}{{\cos }^2}{\rm{x}}}}\) equal to?Where c is the constant of integration.
A.	\({\rm{c}} + \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{a}}\tan {\rm{x}}}}{{\rm{b}}}} \right)\)
B.	\({\rm{c}} - \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{b}}\tan {\rm{x}}}}{{\rm{b}}}} \right)\)
C.	\({\rm{c}} + \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{b}}\tan {\rm{x}}}}{{\rm{a}}}} \right)\)
D.	None of the above
Answer» B. \({\rm{c}} - \frac{1}{{{\rm{ab}}}}{\tan ^{ - 1}}\left( {\frac{{{\rm{b}}\tan {\rm{x}}}}{{\rm{b}}}} \right)\)

What is \(\smallint \frac{{{\rm{dx}}}}{{{{\rm{a}}^2}{{\sin }^2}{\rm{x}} + {{\rm{b}}^2}{{\cos }^2}{\rm{x}}}}\) equal to?Where c is the constant of integration.

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