MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 211 to 220 out of 440 Questions

211.

\int \frac{d x}{x^{2} {(x^{4} + 1)}^{\frac{3}{4}}}

= _____ .

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

212.

\int e^{x} (1 - \cot x + \cot^{2} x) d x

= _____

(a)	$e^{x} \cot x + c$
(b)	$- e^{x} \cot x + c$
(c)	$e^{x} cosec x + c$
(d)	$- e^{x} cosec x + c$

213.

જો

f (x) = \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}}

અને

g (x) = e^{\sin^{- 1} x}

હોય તો,

\int f (x) g (x) d x

= _____

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

214.

\int e^{\sin θ} (\log \sin θ + {cosec}^{2} θ) \cos θ d θ

= _____ .

(a)	$e^{\sin θ} (\log \sin θ + {cosec}^{2} θ) + c$
(b)	$e^{\sin θ} (\log \sin θ + cosec θ) + c$
(c)	$e^{\sin θ} (\log \sin θ - cosec θ) + c$
(d)	$e^{\sin θ} (\log \tan θ - cosec θ) + c$

215.

\int \sqrt{x} e^{\sqrt{x}} d x

= _____ .

(a)	$2 \sqrt{x} - e^{\sqrt{x}} - 4 \sqrt{x} e^{\sqrt{x}} + c$
(b)	$(2 x - 4 \sqrt{x} + 4) e^{\sqrt{x}} + c$
(c)	$(2 x + 4 \sqrt{x} + 4) e^{\sqrt{x}} + c$
(d)	$(1 - 4 \sqrt{x}) e^{\sqrt{x}} + c$

216.

જો

\int [\log (\log x) + \frac{1}{{(\log x)}^{2}}] d x = x [f (x) - g (x)] + c

હોય તો _____

(a)	$f (x) = \log (\log x), g (x) = \frac{1}{\log x}$
(b)	$f (x) = \log x, g (x) = \frac{1}{\log x}$
(c)	$f (x) = \frac{1}{\log x}, g (x) = \log (\log x)$
(d)	$f (x) = \frac{1}{x \log x}, g (x) = \frac{1}{\log x}$

217.

\int \frac{x - 1}{(x - 3) (x - 2)} d x

= _____

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

218.

\int_{\frac{π}{6}}^{\frac{π}{2}} \frac{d x}{1 + \sqrt[3]{\tan^{2} x}}

= _____ .

(a)	$\frac{π}{4}$
(b)	$\frac{π}{12}$
(c)	$\frac{π}{6}$
(d)	$\frac{π}{2}$

219.

\int_{0}^{1} \frac{dx}{x + \sqrt{x}}

= _____

(a)	log 2
(b)	log 4
(c)	log 2
(d)	-log 2

220.

જો

\int_{0}^{a} \frac{1}{1 + 9 x^{2}} d x = \frac{π}{12}

હોય તો a = _____ .

(a)	$\frac{1}{3}$
(b)	$\frac{2}{3}$
(c)	$\frac{1}{6}$
(d)	3

Showing 211 to 220 out of 440 Questions