EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 Feb 2021 Shift 2>Q 43

HARD

JEE Main

IMPORTANT

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If $I_{n} = \int_{\frac{π}{4}}^{\frac{π}{2}} \cot^{n} x d x$ , then

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Important Questions on Definite Integration

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 Feb 2021 Shift 2>Q 44

\lim_{n \to \infty} [\frac{1}{n} + \frac{n}{{(n + 1)}^{2}} + \frac{n}{{(n + 2)}^{2}} + \dots + \frac{n}{{(2 n - 1)}^{2}}]

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 25 Feb 2021 Shift 2>Q 45

The value of

\int_{- 2}^{2} |3 x^{2} - 3 x - 6| d x

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 Feb 2021 Shift 1>Q 46

The value of

\sum_{n = 1}^{100} \int_{n - 1}^{n} e^{x - [x]} d x

, where

[x]

is the greatest integer

\leq x,

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 Feb 2021 Shift 1>Q 47

The value of

\int_{- π / 2}^{π / 2} \frac{\cos^{2} x}{1 + 3^{x}} d x

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 Feb 2021 Shift 1>Q 48

The value of the integral

\int_{0}^{π} |\sin 2 x| d x

is ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 Feb 2021 Shift 2>Q 49

For

x > 0

, if

f (x) = \int_{1}^{x} \frac{\log_{e} t}{(1 + t)} d t

, then

f (e) + f (\frac{1}{e})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 26 Feb 2021 Shift 2>Q 50

If

I_{m, n} = \int_{0}^{1} x^{m - 1} {(1 - x)}^{n - 1} d x

, for

m, n ⩾ 1

, and

\int_{0}^{1} \frac{x^{m - 1} + x^{n - 1}}{{(1 + x)}^{m + n}} d x = α I_{m, n}, α \in R

, then

α

equals ________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 2 September 2020 Shift 1>Q 51

The integral

\int_{0}^{2} ||x - 1| - x| d x

is equal to