1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\sin }^2}x} \over {1 + {2^x}}}} dx$$ is
A
$${\pi \over 4}$$
B
$${\pi \over 8}$$
C
$${\pi \over 2}$$
D
$${4\pi }$$
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
The value of integral $$\int_{{\pi \over 4}}^{{{3\pi } \over 4}} {{x \over {1 + \sin x}}dx}$$ is :
A
$$\pi \sqrt 2$$
B
$$\pi \left( {\sqrt 2 - 1} \right)$$
C
$${\pi \over 2}\left( {\sqrt 2 + 1} \right)$$
D
$$2\pi \left( {\sqrt 2 - 1} \right)$$
3
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
If   $${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$$

$${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$$  and

$${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$$ then
A
I2  >  I3  >  I1
B
I2  >  I1  >  I3
C
I3  >  I2  >  I1
D
I3  >  I1  >  I2
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The value of the integral

$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {{{\sin }^4}} x\left( {1 + \log \left( {{{2 + \sin x} \over {2 - \sin x}}} \right)} \right)dx$$ is :
A
0
B
$${3 \over 4}$$
C
$${3 \over 8}$$ $$\pi$$
D
$${3 \over 16}$$ $$\pi$$
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