MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 391 to 400 out of 440 Questions

391.

\int e^{2 x} \sin x \cos x d x = \frac{e^{2 x}}{8} f (x) + c

તો

f (\frac{π}{4})

= _____

(a)	1
(b)	0
(c)	$\sqrt{2}$
(d)	$\frac{1}{\sqrt{2}}$

392.

\int e^{x} \sin^{2} x d x = A e^{x} + B e^{x} (\cos 2 x + 2 \sin 2 x) + C

તો A+B = _____

(a)	$\frac{2}{5}$
(b)	$\frac{- 2}{5}$
(c)	$\frac{3}{5}$
(d)	$\frac{- 3}{5}$

393.

\int e^{x} \cos x d x = \frac{e^{x}}{2} f (x) + C

તો f(x) ના વિસ્તાર _____ છે.

(a)	[0, 1]
(b)	[-1, 1]
(c)	[-1, 0]
(d)	$[- \sqrt{2}, \sqrt{2}]$

394.

\int e^{- x} \sin^{2} 3 x d x = A e^{- x} + B e^{- x} (6 \sin 6 x - \cos 6 x) + C

તો A+B = _____

(a)	$- \frac{19}{37}$
(b)	$\frac{37}{19}$
(c)	$\frac{18}{37}$
(d)	$\frac{37}{18}$

395.

\int [f (x) g " (x) - f " (x) g (x)] d x

= _____

(a)	$\frac{f (x)}{g' (x)}$
(b)	$f (x) g (x) - f (x) g' (x)$
(c)	$f (x) g' (x) - f' (x) g (x)$
(d)	$f (x) g' (x) + f' (x) g (x)$

396.

\int \cos x \log (\tan \frac{x}{2}) d x

= _____ + c

(a)	$\sin x \log (\tan \frac{x}{2})$
(b)	$\sin x \log (\tan \frac{x}{2}) - x$
(c)	$\sin x \log (\tan \frac{x}{2}) + x$
(d)	આપેલ ઉકેલમાંથી એક પણ નહીં

397.

\int e^{x} . x^{n} d x

= _____ + c

(a)	$e^{x} [x^{n} - n x^{n - 1} + n (n - 1) x^{n - 2} - . . . + {(- 1)}^{n} . n!]$
(b)	$e^{x} [x^{n} - n x^{n - 1} + n (n - 1) x^{n - 2}]$
(c)	$e^{x} x^{n}$
(d)	આપેલ પૈકી એક પણ નહીં.

398.

\int \frac{1}{x (x^{5} + 1)} d x

= _____ + c

(a)	$\frac{1}{5} \log \|\frac{x^{5}}{x^{5} + 1}\|$
(b)	$\log \|\frac{x^{5}}{x^{5} + 1}\|$
(c)	$\frac{1}{6} \log \|\frac{x^{6}}{x^{6} + 1}\|$
(d)	$\log \|\frac{x}{x + 1}\|$

399.

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

= _____ + c

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

400.

જો

\int \frac{d x}{x + x^{7}} = p (x)

, તો

\int \frac{x^{6}}{x + x^{7}} d x

= _____

(a)	In $\|x\| - p (x) + c$
(b)	In $\|x\| + p (x) + c$
(c)	$x - p (x) + c$
(d)	$x + p (x) + c$

Showing 391 to 400 out of 440 Questions