MCQs of Integrals | GUJCET MCQ

Integrals MCQs

MCQs of Integrals

Showing 411 to 420 out of 421 Questions

411.

\int e^{2 x} (logx + \log 2 + \frac{1}{2 x}) dx

=_____+c

(a)	$\frac{e^{2 x}}{x}$
(b)	$e^{2 x} \log 2 x$
(c)	$\frac{1}{2} e^{2 x} \log 2 x$
(d)	None of these

412.

∫{sin(logx)+cos(logx)}dx =_____+c

(a)	xsin(logx)
(b)	xcos(logx)
(c)	sin(logx)
(d)	cos(logx)

413.

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

then

f (\frac{π}{4})

=_____

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

414.

\int e^{- x} \sin^{2} 3 xdx = {Ae}^{- x} + {Be}^{x} (6 \sin 6 x - \cos 6 x) + c

then A+B=_____

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

415.

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

then range of f(x)=_____

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

416.

∫[f(x)g"(x)-f"(x)g(x)]dx=_____

(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)

417.

\int \cos x \log (ten \frac{x}{2}) dx

=_____+c

(a)	$\sin x \log (ten \frac{x}{2})$
(b)	$\sin x \log (ten \frac{x}{2}) - x$
(c)	$\sin x \log (ten \frac{x}{2}) + x$
(d)	None of these

418.

\int e^{x} \cdot x^{n} dx

=_____+c

(a)	$e^{x} [x^{n} - {nx}^{n - 1} + n (n - 1) x^{n - 2} -_____+ (- 1)^{n} \cdot n!]$
(b)	$e^{x} [x^{n} - {nx}^{n - 1} + n (n - 1) x^{n - 2}]$
(c)	$e^{x} x^{n}$
(d)	None of these

419.

\int {(\frac{logx - 1}{1 + (logx)^{2}})}^{2} dx

=_____+c

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

420.

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

=_____+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)	$\log \|\frac{x}{x + 1}\|$

Showing 411 to 420 out of 421 Questions