MCQs of Integrals | GUJCET MCQ

Integrals MCQs

MCQs of Integrals

Showing 261 to 270 out of 421 Questions

261.

\int (x^{5} + 6 x^{4} + 5 x^{3} + 4 x^{2} + 3 x + 1) e^{x} d x

= _____ + c

(a)	$\sum_{i = 1}^{5} x^{i} e^{x}$
(b)	$\sum_{i = 0}^{5} x^{i} e^{x}$
(c)	$\sum_{i = 1}^{6} x^{i} e^{x}$
(d)	$\sum_{i = 0}^{6} x^{i} e^{x}$

262.

\int \tan^{- 1} 2 x d x

= _____ + c

(a)	$x \tan^{- 1} 2 x - \frac{1}{8} \log (1 + 4 x^{2})$
(b)	$x \tan^{- 1} 2 x - \frac{1}{2} \log (1 + 4 x^{2})$
(c)	$x \tan^{- 1} x - \frac{1}{4} \log (1 + 4 x^{2})$
(d)	$x \tan^{- 1} 2 x - \frac{1}{4} \log (1 + 4 x^{2})$

263.

\int e^{x} [\sec x + \log (\sec x + \tan x)] d x

= _____ + c

(a)	$e^{x} \sec x$
(b)	$e^{x} \log (\sec x + \tan x)$
(c)	$\sec x \log (\sec x + \tan x)$
(d)	$e^{x} \sec x \log (\sec x + \tan x)$

264.

\int e^{x} [x^{x} (2 + \log x)] d x

= _____ + c

(a)	$e^{x} \cdot x^{x}$
(b)	$2 e^{x} \cdot x^{x}$
(c)	$e^{x} \log x$
(d)	$e^{x} \cdot x^{x} \log x$

265.

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

= _____ + c

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

266.

\int x \tan^{2} x d x

= _____ + c

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

267.

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

= _____ + c

(a)	$\frac{x^{2} + 1}{2 x} \sqrt{1 - {(x + \frac{1}{x})}^{2}} + \frac{1}{2} \sin^{- 1} \frac{x^{2} + 1}{x}$
(b)	$\frac{x^{2} + 1}{2 x} \sqrt{1 - {(x + \frac{1}{x})}^{2}} + \frac{1}{2} \log \|x + \frac{1}{x} + \sqrt{1 - {(x + \frac{1}{x})}^{2}}\|$
(c)	can not be found
(d)	None of the above

268.

\int (\sin^{2} x + \sin 2 x) e^{x} d x

= _____ + c

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

269.

\int \frac{\cos x}{(1 + \sin x) (2 + \sin x)} d x

= _____ + c

(a)	$\log \|\frac{1 - \sin x}{2 - \sin x}\|$
(b)	$\log \|\frac{1 + \cos x}{2 + \cos x}\|$
(c)	$\log \|\frac{1 + \sin x}{2 + \sin x}\|$
(d)	$\log \|\frac{2 + \sin x}{1 + \sin x}\|$

270.

\int \log_{|a|} x d x

= _____ + c (જ્યાં a < -e)

(a)	$x \log_{\|a\|} e (\log_{e} x - 1)$
(b)	$a \log_{e} \|x\| (\log_{e} x + 1)$
(c)	$x \log_{e} \|a\| (\log_{e} x - 1)$
(d)	$x \log_{\|a\|} x (\log_{e} x - 1)$

Showing 261 to 270 out of 421 Questions