1
WB JEE 2018
+1
-0.25
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
+1
-0.25
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 2017
+1
-0.25
$$\int {\cos (\log x)dx}$$ = F(x) + C, where C is an arbitrary constant. Here, F(x) is equal to
A
$$x[\cos (\log x) + \sin (\log x)]$$
B
$$x[\cos (\log x) - \sin (\log x)]$$
C
$${x \over 2}[\cos (\log x) + \sin (\log x)]$$
D
$${x \over 2}[\cos (\log x) - \sin (\log x)]$$
4
WB JEE 2017
+1
-0.25
$$\int {{{{x^2} - 1} \over {{x^4} + 3{x^2} + 1}}dx}$$ (x > 0) is
A
$${\tan ^{ - 1}}\left( {x + {1 \over x}} \right) + C$$
B
$${\tan ^{ - 1}}\left( {x - {1 \over x}} \right) + C$$
C
$${\log _e}\left| {{{x + {1 \over x} - 1} \over {x + {1 \over x} + 1}}} \right| + C$$
D
$${\log _e}\left| {{{x - {1 \over x} - 1} \over {x - {1 \over x} + 1}}} \right| + C$$
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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