∫- 1117x5 - x4 + 29x3 - 31

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

151.

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

$\frac{1}{8} (x^{2} - 1) + C$
$\frac{x^{2}}{4} + C$
$\frac{x}{2} + C$
$\frac{x^{2}}{2} + C$

152.

$\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{1}{\tan^{3} (x)} dx$ is

$\frac{π}{12}$
$\frac{π}{4}$
$\frac{π}{3}$
$\frac{π}{6}$

Advertisement

153.
$\int_{- 1}^{1} \frac{17 x^{5} - x^{4} + 29 x^{3} - 31 x + 1}{x^{2} + 1} dx$ is

4/5

5/4

4/3

3/4

C.

4/3

$Let I = \int_{- 1}^{1} \frac{17 x^{5} - x^{4} + 29 x^{3} - 31 x + 1}{x^{2} + 1} dx I = \int_{- 1}^{1} \frac{17 x^{5} + 29 x^{3} - 31 x}{x^{2} + 1} dx - \int_{- 1}^{1} \frac{x^{4} - 1}{x^{2} + 1} dx = - 2 \int_{0}^{1} \frac{(x^{2} - 1) (x^{2} + 1)}{x^{2} + 1} dx = - 2 {[(\frac{x^{3}}{3} - x)]}_{0}^{1} = \frac{4}{3}$

Advertisement

154.

If I_n = $\int_{0}^{\frac{π}{4}} \tan^{n} (x) dx$ , then $\frac{1}{I_{3} + I_{5}}$ is

1/4
1/2
1/8
4

Advertisement

155.

If $\int_{0}^{\frac{π}{2}} \sin^{6} (x) dx = \frac{5 π}{32}$ , then the value of $\int_{- π}^{π} (\sin^{6} (x) + \cos^{6} (x)) dx$ is

$\frac{5 π}{8}$
$\frac{5 π}{16}$
$\frac{5 π}{2}$
$\frac{5 π}{4}$

156.

$\int \frac{\sec (x) \csc (x)}{2 \cot (x) - \sec (x) \csc (x)} dx$ is equal to

$\log |\sec (x) + \tan (x)|$ + c
$\log |\sec (x) + \csc (x)|$ + c
$\frac{1}{2} \log |\sec (2 x) + \tan (2 x)|$ + c
$\log |\sec (2 x) + \csc (2 x)|$ + c

157.

If $\int_{0}^{a} (2 a - x) dx = μ and \int_{0}^{a} f (x) dx = λ$ , then $\int_{0}^{2 a} f (x) dx$ equals

$2 λ - μ$
$λ + μ$
$μ - λ$
$λ - 2 μ$

158.

$\int \tan (\sin^{- 1} (x)) dx$ is equal to

$\frac{1}{\sqrt{1 - x^{2}}} + c$
$- \sqrt{1 - x^{2}} + c$
$\frac{- x}{\sqrt{1 - x^{2}}} + c$
$\frac{x}{\sqrt{1 - x^{2}}} + c$

Advertisement

159.

$\int {(\sin (x) - \cos (x))}^{4} (\sin (x) + \cos (x)) dx$ is equal to

$\frac{\sin (x) - \cos (x)}{5} + c$
$\frac{{(\sin (x) - \cos (x))}^{5}}{5}$ + c
$\frac{{(\sin (x) - \cos (x))}^{4}}{4}$ + c
$\frac{{(\sin (x) + \cos (x))}^{5}}{5}$ + c

160.

$\int e^{\sin (θ)} [\log (\sin (θ)) + \csc^{2} (θ)] \cos (θ) dθ$ is equal to

$\int e^{\sin (θ)} [\log (\sin (θ)) + \csc^{2} (θ)] + c$
$e^{\sin (θ)} [\log (\sin (θ)) + \csc (θ)] + c$
$e^{\sin (θ)} [\log (\sin (θ)) - \csc (θ)]$
$e^{\sin (θ)} [\log (\sin (θ)) - \csc^{2} (θ)]$

Advertisement