JEE Main 2019 (Online) 12th January Morning Slot | Definite Integrals and Applications of Integrals Question 232 | Mathematics

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JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, is

$${{15} \over 4}$$

$${{15} \over 2}$$

$${{21} \over 2}$$

$${{17} \over 4}$$

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) in the first quadrant bounded by the parabola, y = x² + 1, the tangent to it at the point (2, 5) and the coordinate axes is :

$${8 \over 3}$$

$${{14} \over 3}$$

$${{187} \over {24}}$$

$${{37} \over {24}}$$

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)

-1

The integral $$\int\limits_{\pi /6}^{\pi /4} {{{dx} \over {\sin 2x\left( {{{\tan }^5}x + {{\cot }^5}x} \right)}}} $$ equals :

$${\pi \over {40}}$$

$${1 \over {20}}{\tan ^{ - 1}}\left( {{1 \over {9\sqrt 3 }}} \right)$$

$${1 \over {10}}\left( {{\pi \over 4} - {{\tan }^{ - 1}}\left( {{1 \over {9\sqrt 3 }}} \right)} \right)$$

$${1 \over 5}\left( {{\pi \over 4}{{-\tan }^{ - 1}}\left( {{1 \over {3\sqrt 3 }}} \right)} \right)$$

JEE Main 2019 (Online) 11th January Morning Slot

MCQ (Single Correct Answer)

-1

The value of the integral $$\int\limits_{ - 2}^2 {{{{{\sin }^2}x} \over { \left[ {{x \over \pi }} \right] + {1 \over 2}}}} \,dx$$ (where [x] denotes the greatest integer less than or equal to x) is

4$$-$$ sin 4

sin 4

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