MCQs of Integrals | GUJCET MCQ

Integrals MCQs

MCQs of Integrals

Showing 391 to 400 out of 421 Questions

391.

If integration of f(x) is e^x and integration of g(x) is cosx, then

\int f (x) cosx dx + \int g (x) e^{x} dx =_____+ c

(a)	f(x)g(x)
(b)	f(x)+g(x)
(c)	e^x
(d)	f(x)-g(x)

392.

If

I = \int e^{x}

sin2x dx then for k=_____ k I= e^x (sinx-2cos 2x)+c

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

393.

If

I_{n} = \int (logx)^{x} dx

then 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

394.

\int e^{\frac{x}{2}} \sin (\frac{x}{2} + \frac{π}{4}) dx =_____+ 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)	$\sqrt{2} e^{\frac{x}{2}} \sin \frac{x}{2}$

395.

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

then

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

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

396.

If

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

then 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)	$\frac{x^{2}}{e} \log \frac{x^{2}}{e}$

397.

\int a^{x} [f' (x) + f (x) loga] dx =_____+c

(a)	$a^{x} \cdot loga f' (x)$
(b)	$a^{x} \cdot f' (x)$
(c)	$a^{x} \cdot f (x)$
(d)	$a^{x} \cdot loga \cdot f (x)$

398.

\sin^{- 1} \frac{1}{x} dx; x > 1 =_____+ c

(a)	x cosec^1-x
(b)	$\log \|x + \sqrt{x^{2} - 1}\|$
(c)	${xcosec}^{- 1} x + \log \|x + \sqrt{x^{2} - 1}\|$
(d)	None of these.

399.

\int \sin \sqrt{x} dx

=_____

(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)	$2 [\sin \sqrt{x} + \cos \sqrt{x}]$

400.

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

=_____+c

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

Showing 391 to 400 out of 421 Questions