MCQs of Integrals

Integrals MCQs

Showing 121 to 130 out of 403 Questions

121.

\int \frac{\sin x}{\sin (x - α)} d x = A x + B \log \sin (x - α) + c

(A,B) = _____

(a)	$(- \cos α, \sin α)$
(b)	$(\cos α, \sin α)$
(c)	$(- \sin α, \cos α)$
(d)	$(\sin α, \cos α)$

122.

\int \frac{d x}{\cos x - \sin x}

= _____ + ci/>

(a) $\frac{1}{\sqrt{2}} \log |\tan (\frac{x}{2} + \frac{3 π}{8})|$

(b) $\frac{1}{\sqrt{2}} \log |\tan (\frac{π}{8} + \frac{x}{2})|$

(c) $\frac{1}{\sqrt{2}} \log |\tan (\frac{x}{2} - \frac{3 π}{8})|$

(d) $\log |\cos \frac{x}{2}|$

123.

\int \frac{d}{\cos x + \sqrt{3} \sin x}

= _____ + c

(a) $\log |\tan (\frac{x}{2} + \frac{π}{12})|$

(b) $\log |\tan (\frac{x}{2} - \frac{π}{12})|$

(c) $\frac{1}{2} \log |\tan (\frac{x}{2} + \frac{π}{12})|$

(d) $\frac{1}{2} \log |\tan (\frac{x}{2} - \frac{π}{12})|$

124.

\int \frac{5 \tan x}{\tan x - 2} d x = x + a \log |\sin x - 2 \cos x| + k

then a = _____

(a) -1

(b) -2

(c) 1

(d) 2

125.

\int f (x) d x = ψ (x), then \int x^{5} f (x^{3}) dx

= _____

(a)	$\frac{1}{3} [x^{3} ψ (x^{3}) - \int x^{2} ψ (x^{3}) d x] + c$
(b)	$\frac{1}{3} x^{3} ψ (x^{3}) - 3 \int x^{3} ψ (x^{3}) d x + c$
(c)	$\frac{1}{3} x^{3} ψ (x^{3}) - \int x^{2} ψ (x^{3}) d x + c$
(d)	$\frac{1}{3} x^{3} ψ (x^{3}) - \int x^{3} ψ (x^{3}) d x + c$

126.

\int \frac{x d x}{2 - x^{2} + \sqrt{2 - x^{2}}}

= _____

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

127.

\int (1 + x - \frac{1}{x}) e^{x + \frac{1}{x}}

dx = _____

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

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

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

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

128.

\int \frac{d x}{{(x + 1)}^{\frac{3}{4}} {(x - 2)}^{\frac{5}{4}}}

= _____

(a)	$4 {(\frac{x + 1}{x - 2})}^{\frac{1}{4}} + C$
(b)	$4 {(\frac{x - 2}{x + 1})}^{\frac{1}{4}} + C$
(c)	$- \frac{4}{3} {(\frac{x + 1}{x - 2})}^{\frac{1}{4}} + C$
(d)	$- \frac{4}{3} {(\frac{x - 2}{x + 1})}^{\frac{1}{4}} + C$

129.

\int \frac{\log (1 + \sqrt{1 + t^{2}})}{\sqrt{1 + t^{2}}} d t = \frac{1}{2} {(g (t))}^{2}

+ C where C is an arbitrary constant, then g(2) = _____

(a) $2 \log (2 + \sqrt{5})$

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

(c) $\frac{1}{\sqrt{5}} \log (2 + \sqrt{5})$

(d) $\frac{1}{2} \log (2 + \sqrt{5})$

130.

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

= _____ + c

(a) $\sqrt{3} \tan^{- 1} (1 + \log x)$

(b) $\frac{2}{\sqrt{3}} \tan^{- 1} (\frac{2 \log x + 1}{\sqrt{3}})$

(c) $\frac{1}{\sqrt{3}} \tan^{- 1} (\frac{\log x + 1}{\sqrt{3}})$

(d) $\frac{1}{\sqrt{3}} s e c^{- 1} (\frac{2 \log x + 1}{\sqrt{3}})$

Showing 121 to 130 out of 403 Questions