1
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
If $$f(x) = \int\limits_0^x {t\left( {\sin x - \sin t} \right)dt\,\,\,}$$ then :
A
f'''(x) + f''(x) = sinx
B
f'''(x) + f''(x) $$-$$ f'(x) = cosx
C
f'''(x) + f'(x) = cosx $$-$$ 2x sinx
D
f'''(x) $$-$$ f''(x) = cosx $$-$$ 2x sinx
2
JEE Main 2018 (Offline)
+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
$${4\pi }$$
3
JEE Main 2018 (Online) 15th April Evening Slot
+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
$$2\pi \left( {\sqrt 2 - 1} \right)$$
4
JEE Main 2018 (Online) 15th April Evening Slot
+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
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