MCQs of Integrals

Integrals MCQs

Showing 101 to 110 out of 421 Questions

101.

\int (\log g (x) - \log |f (x)|) \frac{f (x) g' (x) - g (x) f' (x)}{f (x) g (x)} d x

= _____ + c

(a) $\frac{g (x)}{f (x)}$

(b) $\log |\frac{g (x)}{f (x)}|$

(c) $\frac{1}{2} {[\log |\frac{g (x)}{f (x)}|]}^{2}$

(d) none of these.

102.

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

= _____ + c

(a) $2 \sin^{- 1} (\frac{\log 2}{x})$

(b) $- 2 \sin^{- 1} (\frac{\log 2}{x})$

(c) $- \sin^{- 1} (\frac{x}{\log 2})$

(d) $\sin^{- 1} (\frac{x}{\log 2})$

103.

\int 3^{x + 1} . e^{3 x + 1}

dx = _____ + c

(a) $\frac{3^{x + 1} e^{3 x + 1}}{3 + \log_{e} 3}$

(b) $\frac{3^{x + 1} e^{3 x + 1}}{\log_{e} 3}$

(c) $\frac{3^{x + 1} e^{3 x + 1}}{3 - \log_{e} 3}$

(d) none of these.

104.

\int e^{x \log_{e} 5} e^{x}

dx = _____ + c

(a) $5^{x} e^{x}$

(b) $e^{x \log_{e} 5} e^{x}$

(c) $\frac{(5 e)^{x}}{1 \log_{e} 5}$

(d) $\frac{e^{x}}{1 \log_{e} 5}$

105.

\int \sin^{- 1} (\cos x)

dx = _____ + c , 0< x <1

(a) $\frac{πx - x^{2}}{2}$

(b) $\frac{π}{2} x$

(c) $\frac{πx + x^{2}}{2}$

(d) $\frac{π}{2} x^{2}$

106.

\int {|x|}^{2} d x =

_____

+ c x \in (- 1, 1)

(a)	$\frac{x^{3}}{3}$
(b)	$\frac{{\|x\|}^{3}}{3}$
(c)	does not exist
(d)	none of these.

107.

\int

(x-a) (x-b) (x-c) _____ (x-z) dx is polynomial of power _____

(a) 25

(b) 26

(c) 0

(d) 24

108.

\int {f (3 - 2 x)}^{5} f' (3 - 2 x)

dx = _____ + c

(a) $- \frac{1}{12} {f (3 - 2 x)}^{6}$

(b) $\frac{1}{12} {f (3 - 2 x)}^{6}$

(c) $\frac{1}{6} {f (3 - 2 x)}^{6}$

(d) $- \frac{1}{6} {f (3 - 2 x)}^{6}$

109.

\int \frac{d x}{\sqrt{x (5 + \sqrt{x})}}

= _____ + c

(a) $\frac{1}{2} \sqrt{5 + \sqrt{x}}$

(b) $2 \sqrt{5 + \sqrt{x}}$

(c) $4 \sqrt{5 + \sqrt{x}}$

(d) none of these.

110.

\int \sqrt{\frac{x}{5 - 2 x^{3}}}

dx = _____ + c

(a) $\frac{\sqrt{3}}{5} \sin^{- 1} (\sqrt{\frac{2}{5}} . x^{\frac{3}{2}})$

(b) $\frac{\sqrt{2}}{3} \sin^{- 1} (\sqrt{\frac{2}{5}} . x^{\frac{3}{2}})$

(c) $\frac{\sqrt{2}}{5} \sin^{- 1} (\sqrt{\frac{2}{5}} . x^{\frac{3}{2}})$

(d) none of these.

Showing 101 to 110 out of 421 Questions