∫sin2xsin2x + 2cos2xdx is equal to from Mathe

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Advertisement

Integrals

Multiple Choice Questions

801.

The value of the integral $\int_{- \frac{π}{4}}^{\frac{π}{4}} \log (\sec (θ) - \tan (θ)) dθ$ is

0
$\frac{π}{4}$
$π$
$\frac{π}{2}$

Advertisement

802.
$\int \frac{\sin (2 x)}{\sin^{2} (x) + 2 \cos^{2} (x)} dx$ is equal to

$- \log (1 + \sin^{2} (x)) + C$

$\log (1 + \cos^{2} (x)) + C$

$- \log (1 + \cos^{2} (x)) + C$

$\log (1 + \tan^{2} (x)) + C$

C.

$- \log (1 + \cos^{2} (x)) + C$

$Let I = \int \frac{\sin (2 x)}{\sin^{2} (x) + 2 \cos^{2} (x)} dx = \int \frac{\sin (2 x)}{1 - \cos^{2} (x) + 2 \cos^{2} (x)} dx = \int \frac{\sin (2 x)}{1 + \cos^{2} (x)} dx Put 1 + \cos^{2} (x) = t \Rightarrow - 2 \cos (x) \sin (x) dx = dt \Rightarrow - \sin (2 x) = dt ∴ I = - \int \frac{dt}{t} = - \log (t) + C = - \log (1 + \cos^{2} (x)) + C$

Advertisement

803.

$\int \frac{1}{x^{2} {(x^{4} + 1)}^{\frac{3}{4}}} dx$ is equal to

$\frac{- {(1 + x^{4})}^{\frac{1}{4}}}{2 x} + C$
$\frac{- {(1 + x^{4})}^{\frac{1}{4}}}{x} + C$
$\frac{- {(1 + x^{4})}^{\frac{3}{4}}}{x} + C$
$\frac{- {(1 + x^{4})}^{\frac{1}{4}}}{x^{2}} + C$

804.

$\int_{0}^{\frac{π}{4}} \log (\frac{\sin (x) + \cos (x)}{\cos (x)}) dx$ is equal to

$\int_{0}^{\frac{π}{4}} \log (\frac{\sin (x) + \cos (x)}{\cos (x)}) dx$
$\frac{π}{4} \log (2)$
$\log (2)$
$\frac{π}{2} \log (2)$

Advertisement

805.

$\int \frac{\sin^{2} (x)}{1 + \cos (x)} dx$ is equal to

$\sin (x) + C$
$x + \sin (x) + C$
$\cos (x) + C$
$x - \sin (x) + C$

806.

$\int e^{x} (\frac{1 + \sin (x)}{1 + \cos (x)}) dx$ is equal to

e^x+ C
$e^{x} \tan (\frac{x}{2}) + C$
$e^{x} \sin (x) + C$
$\tan (\frac{x}{2}) + C$

807.

$\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{dx}{1 + \cos (2 x)}$ is equal to

4
2
0
1

808.

The value of $\int \frac{e^{x} (1 + x)}{\cos^{2} (e^{x} . x)} dx$ is equal to

$- \cot ({ex}^{x})$ + C
$\tan (e^{x} . x) + C$
$\tan (e^{x}) + C$
$\cot (e^{x}) + C$

Advertisement

809.

The vate of $\int \frac{e^{x} (x^{2} \tan^{- 1} (x) + \tan^{- 1} (x) + 1)}{x^{2} + 1} dx$ is equal to

$e^{x} \tan^{- 1} (x) + C$
$\tan^{- 1} (e^{x}) + C$
$\tan^{- 1} (x^{e}) + C$
$e^{\tan^{- 1} (x)} + C$

810.

The value of $\int_{- \frac{π}{4}}^{\frac{π}{4}} \sin^{103} (x) . \cos^{101} (x) dx$ is

${(\frac{π}{4})}^{103}$
${(\frac{π}{4})}^{101}$
2
0

Advertisement