1
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
The value of $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx}$$ is:
A
$$\pi$$
B
$${{3\pi \over 2}}$$
C
$${{\pi \over 2}}$$
D
$${{\pi \over 4}}$$
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
The integral
$$\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}$$
is equal to:
A
$$- {1 \over {9}}$$
B
$$- {1 \over {18}}$$
C
$${7 \over {18}}$$
D
$${9 \over 2}$$
3
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$f(x) = \left| {x - 2} \right|$$ and g(x) = f(f(x)), $$x \in \left[ {0,4} \right]$$. Then
$$\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx$$ is equal to:
A
1
B
0
C
$${1 \over 2}$$
D
$${3 \over 2}$$
4
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If the value of the integral
$$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$

is $${k \over 6}$$, then k is equal to :
A
$$2\sqrt 3 + \pi$$
B
$$3\sqrt 2 - \pi$$
C
$$3\sqrt 2 + \pi$$
D
$$2\sqrt 3 - \pi$$
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