JEE Main 2017 (Online) 8th April Morning Slot | Definite Integrals and Applications of Integrals Question 257 | Mathematics

JEE Main 2017 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

The integral $$\int_{{\pi \over {12}}}^{{\pi \over 4}} {\,\,{{8\cos 2x} \over {{{\left( {\tan x + \cot x} \right)}^3}}}} \,dx$$ equals :

$${{15} \over {128}}$$

$${{15} \over {64}}$$

$${{13} \over {32}}$$

$${{13} \over {256}}$$

JEE Main 2017 (Offline)

MCQ (Single Correct Answer)

-1

The integral $$\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}} $$ is equal to

$$-$$ 1

$$-$$ 2

JEE Main 2017 (Offline)

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region

$$\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}$$ is

$${3 \over 2}$$

$${7 \over 3}$$

$${5 \over 2}$$

$${59 \over 12}$$

JEE Main 2016 (Online) 10th April Morning Slot

MCQ (Single Correct Answer)

-1

The value of the integral

$$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$$

where [x] denotes the greatest integer less than or equal to x, is :

$${1 \over 3}$$

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