JEE Main 2019 (Online) 9th April Evening Slot | Definite Integrals and Applications of Integrals Question 223 | Mathematics

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JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

The value of the integral $$\int\limits_0^1 {x{{\cot }^{ - 1}}(1 - {x^2} + {x^4})dx} $$ is :-

$${\pi \over 2} - {1 \over 2}{\log _e}2$$

$${\pi \over 4} - {\log _e}2$$

$${\pi \over 4} - {1 \over 2}{\log _e}2$$

$${\pi \over 2} - {\log _e}2$$

JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

If f : R $$ \to $$ R is a differentiable function and f(2) = 6,
then $$\mathop {\lim }\limits_{x \to 2} {{\int\limits_6^{f\left( x \right)} {2tdt} } \over {\left( {x - 2} \right)}}$$ is :-

2f'(2)

24f'(2)

12f'(2)

JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region
A = {(x, y) : $${{y{}^2} \over 2}$$ $$ \le $$ x $$ \le $$ y + 4} is :-

$${{53} \over 3}$$

JEE Main 2019 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

The value of $$\int\limits_0^{\pi /2} {{{{{\sin }^3}x} \over {\sin x + \cos x}}dx} $$ is

$${{\pi - 2} \over 8}$$

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

$${{\pi - 1} \over 2}$$

$${{\pi - 1} \over 4}$$

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