MCQs of Integrals

Integrals MCQs

Showing 171 to 180 out of 403 Questions

171.

\int \frac{x^{5}}{\sqrt{1 - x^{3}}}

dx = _____ + c

(a) $\frac{2}{3} \sqrt{1 - x^{3}} - \frac{2}{9} {(1 - x^{3})}^{\frac{3}{2}}$

(b) $\frac{2}{3} (2 + x^{3}) \sqrt{1 - x^{3}}$

(c) $- \frac{2}{9} (2 + x^{3}) \sqrt{1 - x^{3}}$

(d) none of these.

172.

\int \frac{e^{x}}{\sqrt{x}} (1 + 2 x) d x

= _____ + c

(a) $\sqrt{x} e^{x}$

(b) $\frac{e^{x}}{\sqrt{x}}$

(c) $2 e^{x} \sqrt{x}$

(d) xe^x

173.

\int

log x (log x + 2) dx = _____ + c

(a)	x (log x)²
(b)	x (1 + log x)²
(c)	x [1 + (log x²)]
(d)	$\frac{\log x}{x}$

174.

\int

x^4x (1 + log x) dx = _____ + c

(a)	$\frac{x^{4 x}}{4}$
(b)	$\frac{x^{3 x}}{3}$
(c)	4x^5x
(d)	x^x (1 + log x)

175.

If I_{n} = \int \cot^{n} x d x then, I_{0} + I_{1} + 2 (I_{2} + I_{3}) + I_{4} + I_{5}

= _____ (where u = cotx)

(a)	$- (u + \frac{u^{2}}{2} + \frac{u^{3}}{3} + \frac{u^{4}}{4})$
(b)	1 + u + u²+ u³
(c)	- (u + u²+ u³ + u⁴)
(d)	$\frac{1}{u} + \frac{1}{u^{2}} + \frac{1}{u^{3}} + \frac{1}{u^{4}}$

176.

\int \frac{f (x)}{x^{3} - 1} d x

= _____ + c where f(x) is a quadratic polynomial in x f(0) = f(1) = - 3 and f(2) = - 1

(a)	$\log \|\frac{x^{2} + x + 1}{x - 1}\| + \frac{2}{\sqrt{3}} \tan^{- 1} (\frac{2 (x + 1)}{\sqrt{3}})$
(b)	$\log \|\frac{x^{2} + 1}{x - 1}\| + \frac{1}{\sqrt{3}} \tan^{- 1} (\frac{x + 1}{2 \sqrt{3}})$
(c)	$\log \|\frac{x - 1}{x^{2} + x + 1}\| + \frac{1}{\sqrt{3}} \tan^{- 1} (\frac{2 x - 1}{2})$
(d)	$\log \|\frac{x^{2} - x - 1}{x + 1}\| + \frac{2}{\sqrt{3}} \tan^{- 1} (\frac{2 x - 1}{\sqrt{3}})$

177.

\int \frac{1}{e^{x} - 1} d x

= _____ + c

(a)	log (e^x - 1) - x
(b)	log (e^x + 1) - x
(c)	log e^x - x
(d)	log (e^x - x) - 1

178.

\int \{\cos^{- 1} x + \cos^{- 1} \sqrt{1 - x^{2}}\} d x, \forall x \in [- 1, 0)

= _____ + c

(a)	$\frac{π}{2} x - 2 x \sin^{- 1} x + 2 \{- \sqrt{1 - x^{2}}\}$
(b)	$\frac{π}{2} x + x \sin^{- 1} x - 2 \sqrt{1 + x^{2}}$
(c)	$\frac{π}{2} x - 2 x \cos^{- 1} x - 2 \sqrt{1 - x^{2}}$
(d)	$\frac{π}{2} x + 2 x \sin^{- 1} x + 2 \sqrt{1 - x^{2}}$

179.

If \int \frac{dx}{(x^{2} + 1) (x^{2} + 4)} = {Atan}^{- 1} x + {Btan}^{- 1} \frac{x}{2} + C then A + B

= _____

(a)	$\frac{1}{3}$
(b)	$\frac{1}{6}$
(c)	$- \frac{1}{6}$
(d)	$- \frac{1}{3}$

180.

\int \sqrt{x^{2} - 8 x + 7} d x

= _____ + c

(a)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} + 9 \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$
(b)	$\frac{1}{2} (x + 4) \sqrt{x^{2} - 8 x + 7} + 9 \log \|x + 4 + \sqrt{x^{2} - 8 x + 7}\|$
(c)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} - 3 \sqrt{2} \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$
(d)	$\frac{1}{2} (x - 4) \sqrt{x^{2} - 8 x + 7} - \frac{9}{2} \log \|x - 4 + \sqrt{x^{2} - 8 x + 7}\|$

Showing 171 to 180 out of 403 Questions