1
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$2\pi \left( {\sqrt 2 - 1} \right)$$
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The area (in sq. units) of the region

{x $$ \in $$ R : x $$ \ge $$ 0, y $$ \ge $$ 0, y $$ \ge $$ x $$-$$ 2  and y $$ \le $$ $$\sqrt x $$}, is :
A
$${{13} \over 3}$$
B
$${{8} \over 3}$$
C
$${{10} \over 3}$$
D
$${{5} \over 3}$$
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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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