EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 7th April 2013>Q 103

MEDIUM

JEE Main

IMPORTANT

Earn 100

Statement - I : The value of the integral $\int_{π / 6}^{π / 3} \frac{d x}{1 + \sqrt{\tan x}}$ is equal to $\frac{π}{6} .$

Statement - II : $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x .$

60% studentsanswered this correctly

Important Questions on Definite Integration

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 24 June 2022 Shift 1>Q 104

If

f (θ) = \sin θ + \int_{- \frac{π}{2}}^{\frac{π}{2}} (\sin θ + t \cos θ) \cdot f (t) d θ

, then

|\int_{0}^{\frac{π}{2}} f (θ) d θ|

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 24 June 2022 Shift 1>Q 105

Let

\underset{0 ⩽ x ⩽ 2}{Max} \{\frac{9 - x^{2}}{5 - x}\} = α

and

\underset{0 ⩽ x ⩽ 2}{Min} \{\frac{9 - x^{2}}{5 - x}\} = β

. If

\int_{β - \frac{8}{3}}^{2 α - 1} Max \{\frac{9 - x^{2}}{5 - x}, x\} d x = α_{1} + α_{2} \log_{e} (\frac{8}{15})

, then

α_{1} + α_{2}

is equal to ______

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 24 June 2022 Shift 2>Q 106

The value of the integral

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{d x}{(1 + e^{x}) (\sin^{6} x + \cos^{6} x)}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 24 June 2022 Shift 2>Q 107

\lim_{n \to \infty} (\frac{n^{2}}{(n^{2} + 1) (n + 1)} + \frac{n^{2}}{(n^{2} + 4) (n + 2)} + \frac{n^{2}}{(n^{2} + 9) (n + 3)} + \dots + \frac{n^{2}}{(n^{2} + n^{2}) (n + n)})

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 June 2022 Shift 1>Q 108

The value of

\int_{0}^{π} \frac{e^{\cos x} \sin x}{(1 + \cos^{2} x) (e^{\cos x} + e^{- \cos x})} d x

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 June 2022 Shift 2>Q 109

If

b_{n} = \int_{0}^{\frac{π}{2}} \frac{\cos^{2} n x}{\sin x} d x, n \in ℕ

, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 June 2022 Shift 2>Q 110

The value of

b > 3

for which

12 \int_{3}^{b} \frac{1}{(x^{2} - 1) (x^{2} - 4)} d x = \log_{e} (\frac{49}{40})

, is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 June 2022 Shift 2>Q 111

The integral

\frac{24}{π} \int_{0}^{\sqrt{2}} \frac{(2 - x^{2}) dx}{(2 + x^{2}) \sqrt{4 + x^{4}}}

is equal to ______.