EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 11th April 2015>Q 97

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JEE Main

IMPORTANT

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Let $f : R \to R$ be a function such that $f (2 - x) = f (2 + x)$ and $f (4 - x) = f (4 + x)$ , for all $x \in R$ and $\int_{0}^{2} f (x) d x = 5$ . Then the value of $\int_{10}^{50} f (x) d x$ is

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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 - 11th April 2015>Q 98

Let

f : (- 1, 1) \to R

be a continuous function. If

\int_{0}^{\sin x} f (t) d t = \frac{\sqrt{3}}{2} x,

then

f (\frac{\sqrt{3}}{2})

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 19th April 2014>Q 99

Let, the function

F

be defined as

F (x) = \int_{1}^{x} \frac{e^{t}}{t} d t, x > 0,

then the value of the integral

\int_{1}^{x} \frac{e^{t}}{t + a} d t,

where

a > 0,

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 9th April 2014>Q 100

The integral

\int_{0}^{\frac{1}{2}} \frac{\ln (1 + 2 x)}{1 + 4 x^{2}} d x

equals

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 6th April 2014>Q 101

The integral

\int_{0}^{π} \sqrt{1 + 4 {sin}^{2} \frac{x}{2} - 4 sin \frac{x}{2}} d x

equals

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main - 7th April 2013>Q 102

The intercepts on the

x

-axis made by tangents to the curve,

y = \int_{0}^{x} |t| d t, x \in R,

which are parallel to the line

y = 2 x

, are equal to

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JEE Main

IMPORTANT

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

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

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 ______