MCQs of Integrals

Integrals MCQs

Showing 181 to 190 out of 403 Questions

181.

\int x^{2 n - 1} \sin x^{n} d x

= _____ + c

(a)	$\frac{1}{n} [- x^{n} \cos x^{n} + \sin x^{n}]$
(b)	$\frac{1}{n} [x \cos x^{n} - \sin x^{n}]$
(c)	$\frac{1}{n} [- x^{n} \sin x^{n} + \cos x^{n}]$
(d)	$\frac{1}{n} [\cos x^{n} + \sin x^{n}]$

182.

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

_____

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

183.

\int \frac{d x}{1 + \sqrt[3]{x}}

= _____ + c

(a) $\frac{1}{2} x^{\frac{2}{3}} - \sqrt[3]{x} + \log |\sqrt[3]{x} + 1|$

(b) $\frac{3}{2} x^{\frac{2}{3}} + 3 \sqrt[3]{x} + 3 \log |\sqrt[3]{x} + 1|$

(c) $\frac{2}{3} x^{\frac{2}{3}} - 3 \sqrt[3]{x} + 3 \log |\sqrt[3]{x} + 1|$

(d) none of these.

184.

\int \frac{\sin x + \cos x}{\sqrt{\sin 2 x}}

dx = _____

(a) $\sin^{- 1} (\sin x - \cos x)$

(b) $\sin^{- 1} (\sin x + \cos x)$

(c) $\sin^{- 1} (\cos x - \sin x)$

(d) none of these.

185.

\int \frac{1}{{(\sin x)}^{\frac{3}{5}} {(\cos x)}^{\frac{7}{5}}}

dx = _____ + c

(a) $\frac{5 {(\tan x)}^{\frac{7}{5}}}{7}$

(b) $\frac{5 {(\tan x)}^{\frac{2}{5}}}{2}$

(c) $= \frac{5 {(\cot x)}^{\frac{2}{5}}}{2}$

(d) $\frac{5 {(c o t x)}^{\frac{7}{5}}}{7}$

186.

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

,then f(x) = _____

(a) $\frac{1}{x^{2} + 1}$

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

(c) $\frac{1}{{(x^{2} + 1)}^{2}}$

(d) none of these.

187.

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

dx = _____ + c

(a) $\sin^{- 1} x + \sqrt{1 - x^{2}}$

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

(c) $\cos^{- 1} x + \sqrt{1 - x^{2}}$

(d) $\cos^{- 1} x + 2 \sqrt{1 - x^{2}}$

188.

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

189.

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

190.

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

Showing 181 to 190 out of 403 Questions