JEE Main 2022 (Online) 26th June Morning Shift | Definite Integrals and Applications of Integrals Question 96 | Mathematics

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JEE Main 2022 (Online) 26th June Morning Shift

MCQ (Single Correct Answer)

-1

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

$$4(2\sqrt 3 + \sqrt 6 - 4)$$

$$4(4\sqrt 3 + \sqrt 6 - 4)$$

$$8(4\sqrt 3 + 3\sqrt 6 - 9)$$

$$8(4\sqrt 3 + \sqrt 6 - 9)$$

JEE Main 2022 (Online) 25th June Evening Shift

MCQ (Single Correct Answer)

-1

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

$${1 \over {3}}$$

$${1 \over {6}}$$

$${2 \over {3}}$$

$${3 \over {4}}$$

JEE Main 2022 (Online) 25th June Morning Shift

MCQ (Single Correct Answer)

-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:

$${{{\pi ^2}} \over 4}$$

$${{{\pi ^2}} \over 2}$$

$${\pi \over 4}$$

$${\pi \over 2}$$

JEE Main 2022 (Online) 24th June Evening Shift

MCQ (Single Correct Answer)

-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

2$$\pi$$

$$\pi$$

$${\pi \over 2}$$

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