1
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\int {{e^{\sin x}}} .\left[ {{{x{{\cos }^3}x - \sin x} \over {{{\cos }^2}x}}} \right]dx = {e^{\sin x}}f(x) + c$$, where c is constant of integration, then f(x) is equal to
A
sec x $$-$$ x
B
x $$-$$ sec x
C
tan x $$-$$ x
D
x $$-$$ tan x
2
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$\int {f(x)} \sin x\cos xdx = {1 \over {2({b^2} - {a^2})}}\log (f(x)) + c$$, where c is the constant of integration, then f(x) is equal to
A
$${2 \over {({b^2} - {a^2})\sin 2x}}$$
B
$${2 \over {ab\sin 2x}}$$
C
$${2 \over {({b^2} - {a^2})\cos 2x}}$$
D
$${2 \over {ab\cos 2x}}$$
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
If $$M = \int\limits_0^{\pi /2} {{{\cos x} \over {x + 2}}dx} $$, $$N = \int\limits_0^{\pi /4} {{{\sin x\cos x} \over {{{(x + 1)}^2}}}dx} $$, then the value of M $$-$$ N is
A
$$\pi$$
B
$${\pi \over 4}$$
C
$${2 \over {\pi - 4}}$$
D
$${2 \over {\pi + 4}}$$
4
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of the integral $$I = \int_{1/2014}^{2014} {{{{{\tan }^{ - 1}}x} \over x}} dx$$ is
A
$${\pi \over 4}$$log2014
B
$${\pi \over 2}$$log2014
C
$$\pi$$log2014
D
$${{1 \over 2}}$$log2014
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