MCQs of સંકલન | GUJCET MCQ

સંકલન MCQs

MCQs of સંકલન

Showing 361 to 370 out of 428 Questions

361.

જો

I_{n} = \int {(\log x)}^{n} d x

તો

I_{n} + n I_{n - 1}

= _____

(a)	$x {(\log x)}^{n}$
(b)	${(x \log x)}^{n}$
(c)	${(\log x)}^{n - 1}$
(d)	$n {(\log x)}^{n}$

362.

\int e^{\frac{x}{2}} \sin (\frac{x}{2} + \frac{π}{4}) d x

= _____ + c

(a)	$e^{\frac{x}{2}} \cos \frac{x}{2}$
(b)	$\sqrt{2} e^{\frac{x}{2}} \cos \frac{x}{2}$
(c)	$e^{\frac{x}{2}} \sin \frac{x}{2}$
(d)	$\sqrt{2} e^{\frac{x}{2}} \sin \frac{x}{2}$

363.

જો

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

તો

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

= _____ + c

(a)	$\frac{1}{2} {\{f (x)\}}^{2}$
(b)	${\{g (x)\}}^{2}$
(c)	${\{f (x)\}}^{2}$
(d)	$\frac{1}{2} {\{g (x)\}}^{2}$

364.

જો

\frac{d}{d x} f (x) = x \log x

તો

f (x)

= _____ + c

(a)	$x^{2} \log \frac{x^{2}}{e}$
(b)	$\frac{x^{2}}{2} \log \frac{x^{2}}{e}$
(c)	$\frac{x^{2}}{4} \log \frac{x^{2}}{e}$
(d)	$\frac{x^{2}}{e} \log \frac{x^{2}}{e}$

365.

\int a^{x} [f' (x) + f (x) \log a] d x =_____+ c . (a \in R^{+} - \{1\})

(a)	$a^{x} . \log a f' (x)$
(b)	$a^{x} . f' (x)$
(c)	$a^{x} . f (x)$
(d)	$a^{x} . \log a . f (x)$

366.

\sin^{- 1} \frac{1}{x} d x

; x > 1 = _____ + c

(a)	$x {cosec}^{- 1} x$
(b)	$\log \|x + \sqrt{x^{2} - 1}\|$
(c)	$x {cosec}^{- 1} x + \log \|x + \sqrt{x^{2} - 1}\|$
(d)	આપેલ પૈકી એક પણ નહીં.

367.

\int \sin \sqrt{x} d x

= _____

(a)	$2 [\sin \sqrt{x} - \sqrt{x} \cos \sqrt{x}]$
(b)	$2 [\sin \sqrt{x} - \cos \sqrt{x}]$
(c)	$2 [\sin \sqrt{x} + \sqrt{x} \cos \sqrt{x}]$
(d)	$2 [\sin \sqrt{x} + \cos \sqrt{x}]$

368.

\int 3^{x} \sqrt{9^{x} - 1} d x = k 3^{x} \sqrt{9^{x} - 1} - k \log |3^{x} + \sqrt{9^{x} - 1}| + c

તો k = _____

(a)	$\frac{1}{2 \log 3}$
(b)	2log3
(c)	$2 \log_{3}^{e}$
(d)	$3 \log_{2}^{e}$

369.

\int \sqrt{x^{2} - 6} d x

= _____ + c

(a)	$\frac{x}{2} \sqrt{x^{2} - 6} - 3 \sin^{- 1} (\frac{x}{\sqrt{6}})$
(b)	$\frac{x}{2} \sqrt{x^{2} - 6} - 3 \log \|x + \sqrt{x^{2} - 6}\|$
(c)	$\frac{x}{2} \sqrt{x^{2} - 6} + 3 \log \|x + \sqrt{x^{2} - 6}\|$
(d)	$\frac{x}{2} \sqrt{x^{2} - 6} + 3 \sin^{- 1} (\frac{x}{\sqrt{6}})$

370.

\int \cos x \sqrt{4 - \sin^{2} x} d x = f (x) \sqrt{4 - \sin^{2} x} + 2 \sin^{- 1} (f (x)) + c

તો f(x) = _____

(a)	x²
(b)	sin²x
(c)	sinx
(d)	$\frac{1}{2} \sin x$

Showing 361 to 370 out of 428 Questions