1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

The area bounded by the curve y = |x2 $$-$$ 9| and the line y = 3 is :

A
$$4(2\sqrt 3 + \sqrt 6 - 4)$$
B
$$4(4\sqrt 3 + \sqrt 6 - 4)$$
C
$$8(4\sqrt 3 + 3\sqrt 6 - 9)$$
D
$$8(4\sqrt 3 + \sqrt 6 - 9)$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

The area of the region enclosed between the parabolas y2 = 2x $$-$$ 1 and y2 = 4x $$-$$ 3 is

A
$${1 \over {3}}$$
B
$${1 \over {6}}$$
C
$${2 \over {3}}$$
D
$${3 \over {4}}$$
3
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
$${\pi \over 2}$$
4
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
$${\pi \over 2}$$
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