MCQs of Integrals

Integrals MCQs

Showing 191 to 200 out of 421 Questions

191.

\int e^{4 \log} {(x^{5} + 1)}^{- 1}

dx = _____ + c

(a) $\log |x^{5} + 1|$

(b) $\frac{1}{5} \log |x^{5} + 1|$

(c) $- \log |x^{5} + 1|$

(d) $- \frac{4}{{(x^{5} + 1)}^{2}}$

192.

\int s e c^{2} (3 - \frac{1}{5} x)

dx = _____ + c

(a) $\tan (3 - \frac{x}{5})$

(b) $- 5 \tan (3 - \frac{x}{5})$

(c) $5 \tan (3 - \frac{x}{5})$

(d) $- \frac{1}{5} \tan (3 - \frac{x}{5})$

193.

\int \frac{x - 1}{\sqrt{x + 4}}

dx = _____ + c where x + 4 > 0

(a) $\frac{2}{3} {(x + 1)}^{\frac{3}{2}} + 5 \sqrt{x + 4}$

(b) $\frac{2}{3} {(x + 4)}^{\frac{3}{2}} + 10 \sqrt{x + 4}$

(c) $\frac{2}{3} {(x + 4)}^{\frac{3}{2}} - 5 \sqrt{x + 4}$

(d) $\frac{2}{3} {(x + 4)}^{\frac{3}{2}} - 10 \sqrt{x + 4}$

194.

\int \frac{{(x - 1)}^{2}}{{(x^{2} + 1)}^{2}} d x = \tan^{- 1} x + f (x) + c t h e n f (x)

= _____

(a)	$\tan^{- 1} x + \frac{1}{x^{2} + 1}$
(b)	$\frac{1}{{(x^{2} + 1)}^{2}}$
(c)	$\frac{1}{x^{2} + 1}$
(d)	none of these

195.

\int \frac{{(\sin x)}^{2010}}{{(\cos x)}^{2012}}

dx = _____ + c

(a) $\frac{{(\tan x)}^{2008}}{2008}$

(b) $\frac{{(\tan x)}^{2}}{2}$

(c) $\frac{{(\tan x)}^{2009}}{2009}$

(d) $\frac{{(\tan x)}^{2011}}{2011}$

196.

\int \frac{x \cos x}{(x \sin x + c o s x + 7)}

dx = _____ + c

197.

\int e^{sinθ} (\log \sin θ + {cosec}^{2} θ) \cos θdθ =___+ c

(a)	$\int e^{sinθ} (\log \sin θ + {codec}^{2} θ)$
(b)	$\int e^{sinθ} (\log \sin θ + \cos ec θ)$
(c)	$\int e^{sinθ} (\log \sin θ - \cos ec θ)$
(d)	$\int e^{sinθ} (\log \sin θ - \cos {ec}^{2} θ)$

198.

I = \int_{\frac{- π}{2}}^{\frac{π}{2}} |\sin x| dx =_____

(a)	0
(b)	2
(c)	-2
(d)	-2 < I <2

199.

\int_{- 100}^{100} f (x) dx =_____

(a)	$\int_{- 100}^{100} f (x^{2}) dx$
(b)	$\int_{- 100}^{100} f (- x^{2}) dx$
(c)	$\int_{- 100}^{100} f (\frac{1}{x}) dx$
(d)	$\int_{- 100}^{100} f (- x) dx$

200.

\int_{0}^{2} (x - 2 | + [x])

dx = _____

(a)	2
(b)	3
(c)	1
(d)	4

Showing 191 to 200 out of 421 Questions