1
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The value of the integral $$\int\limits_0^1 {x{{\cot }^{ - 1}}(1 - {x^2} + {x^4})dx}$$ is :-
A
$${\pi \over 2} - {1 \over 2}{\log _e}2$$
B
$${\pi \over 4} - {\log _e}2$$
C
$${\pi \over 4} - {1 \over 2}{\log _e}2$$
D
$${\pi \over 2} - {\log _e}2$$
2
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If f : R $$\to$$ R is a differentiable function and f(2) = 6,
then $$\mathop {\lim }\limits_{x \to 2} {{\int\limits_6^{f\left( x \right)} {2tdt} } \over {\left( {x - 2} \right)}}$$ is :-
A
2f'(2)
B
24f'(2)
C
0
D
12f'(2)
3
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
The value of $$\int\limits_0^{\pi /2} {{{{{\sin }^3}x} \over {\sin x + \cos x}}dx}$$ is
A
$${{\pi - 2} \over 8}$$
B
$${{\pi - 2} \over 4}$$
C
$${{\pi - 1} \over 2}$$
D
$${{\pi - 1} \over 4}$$
4
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let $$f(x) = \int\limits_0^x {g(t)dt}$$ where g is a non-zero even function. If ƒ(x + 5) = g(x), then $$\int\limits_0^x {f(t)dt}$$ equals-
A
5$$\int\limits_{x + 5}^5 {g(t)dt}$$
B
$$\int\limits_{x + 5}^5 {g(t)dt}$$
C
$$\int\limits_{5}^{x+5} {g(t)dt}$$
D
2$$\int\limits_{5}^{x+5} {g(t)dt}$$
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