1
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

The value of $$\int\limits_0^\pi {{{{e^{\cos x}}\sin x} \over {(1 + {{\cos }^2}x)({e^{\cos x}} + {e^{ - \cos x}})}}dx}$$ is equal to:

A
$${{{\pi ^2}} \over 4}$$
B
$${{{\pi ^2}} \over 2}$$
C
$${\pi \over 4}$$
D
$${\pi \over 2}$$
2
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

The value of the integral

$$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {(1 + {e^x})({{\sin }^6}x + {{\cos }^6}x)}}}$$ is equal to

A
2$$\pi$$
B
0
C
$$\pi$$
D
$${\pi \over 2}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1
Out of Syllabus

$$\mathop {\lim }\limits_{n \to \infty } \left( {{{{n^2}} \over {({n^2} + 1)(n + 1)}} + {{{n^2}} \over {({n^2} + 4)(n + 2)}} + {{{n^2}} \over {({n^2} + 9)(n + 3)}} + \,\,....\,\, + \,\,{{{n^2}} \over {({n^2} + {n^2})(n + n)}}} \right)$$ is equal to :

A
$${\pi \over 8} + {1 \over 4}{\log _e}2$$
B
$${\pi \over 4} + {1 \over 8}{\log _e}2$$
C
$${\pi \over 4} - {1 \over 8}{\log _e}2$$
D
$${\pi \over 8} + {\log _e}\sqrt 2$$
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Let f : R $$\to$$ R be a continuous function. Then $$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{{\pi \over 4}\int\limits_2^{{{\sec }^2}x} {f(x)\,dx} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ is equal to :
A
f (2)
B
2f (2)
C
2f $$\left( {\sqrt 2 } \right)$$
D
4f (2)
EXAM MAP
Medical
NEET