EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 8th April 2019 Shift 1>Q 71

MEDIUM

JEE Main

IMPORTANT

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If $f (x) = \frac{2 - x c o s x}{2 + x c o s x}$ and $g (x) = \log_{e} x,$ then the value of the integral $\int_{- \frac{π}{4}}^{\frac{π}{4}} g (f (x)) d x$ is

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Important Questions on Definite Integration

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 8th April 2019 Shift 2>Q 72

Let

f (x) = \int_{0}^{x} g (t) d t,

where

g

is a non-zero even function. If

f (x + 5) = g (x),

then

\int_{0}^{x} f (t) d t

equals

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 10th April 2019 Shift 1>Q 73

The value of

\int_{0}^{2 π} [\sin 2 x (1 + \cos 3 x)] d x

, where

[t]

denotes the greatest integer function is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 10th April 2019 Shift 1>Q 74

\underset{n \to \infty}{l i m} (\frac{{(n + 1)}^{1 / 3}}{n^{4 / 3}} + \frac{{(n + 2)}^{1 / 3}}{n^{4 / 3}} + . . . . . + \frac{{(2 n)}^{1 / 3}}{n^{4 / 3}})

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 10th April 2019 Shift 2>Q 75

The integral

\int_{\frac{π}{6}}^{\frac{π}{3}} {s e c}^{\frac{2}{3}} x \cdot c o s e c^{\frac{4}{3}} x d x

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 10th January 2019 Shift 2>Q 76

The value of

\int_{- π / 2}^{π / 2} \frac{d x}{[x] + [\sin x] + 4},

where

[t]

denotes the greatest integer less than or equal to

t,

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 10th January 2019 Shift 2>Q 77

If

\int_{0}^{x} f (t) d t = x^{2} + \int_{x}^{1} t^{2} f (t) d t,

then

f^{'} (\frac{1}{2})

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 12th April 2019 Shift 1>Q 78

Let

f : R \to R

be a continuous and differentiable function such that

f (2) = 6

and

f^{'} (2) = \frac{1}{48}

. If

\int_{6}^{f (x)} 4 t^{3} d t = (x - 2) g (x),

then

\underset{x \to 2}{l i m} g (x)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 12th April 2019 Shift 1>Q 79

If

\int_{0}^{\frac{π}{2}} \frac{c o t x}{c o t x + cosec x} d x = m (π + n),

then

m n

is equal to