EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 16 March 2021 Shift 1>Q 27

MEDIUM

JEE Main

IMPORTANT

Earn 100

If the normal to the curve $y (x) = \int_{0}^{x} (2 t^{2} - 15 t + 10) d t$ at a point $(a, b)$ is parallel to the line $x + 3 y = - 5, a > 1$ , then the value of $|a + 6 b|$ is equal to ________.

50% studentsanswered this correctly

Important Questions on Definite Integration

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 16 March 2021 Shift 1>Q 28

Let

f : R \to R

be a continuous function such that

f (x) + f (x + 1) = 2

for all

x \in R

. If

I_{1} = \int_{0}^{8} f (x) d x

and

I_{2} = \int_{- 1}^{3} f (x) d x

, then the value of

I_{1} + 2 I_{2}

is equal to ________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 16 March 2021 Shift 2>Q 29

Consider the integral $I = \int_{0}^{10} \frac{[x] e^{[x]}}{e^{x - 1}} d x$ where $[x]$ denotes the greatest integer less than or equal to $x$ . Then the value of $I$ is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 16 March 2021 Shift 2>Q 30

Let

P (x) = x^{2} + b x + c

be a quadratic polynomial with real coefficients such that

\int_{0}^{1} P (x) d x = 1

and

P (x)

leaves remainder

5

when it is divided by

(x - 2)

. Then the value of

9 (b + c)

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 17 March 2021 Shift 1>Q 31

Which of the following statement is correct for the function

g (α)

for

α \in R

such that

g (α) = \int_{\frac{π}{6}}^{\frac{π}{3}} \frac{\sin^{α} x}{\cos^{α} x + \sin^{α} x} d x

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 17 March 2021 Shift 1>Q 32

If

[\cdot]

represents the greatest integer function, then the value of

|\int_{0}^{\sqrt{\frac{π}{2}}} [[x^{2}] - \cos x] d x|

is ___________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 17 March 2021 Shift 2>Q 33

Let

f : R \to R

be defined as

f (x) = e^{- x} \sin x .

If

F : [0, 1] \to R

is a differentiable function such that

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

then the value of

\int_{0}^{1} (F^{'} (x) + f (x)) e^{x} d x

lies in the interval

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 17 March 2021 Shift 2>Q 34

If the integral

\int_{0}^{10} \frac{[\sin 2 π x]}{e^{x - [x]}} d x = α e^{- 1} + β e^{- \frac{1}{2}} + γ,

where

α, β, γ

are integers and

[x]

denotes the greatest integer less than or equal to

x,

then the value of

α + β + γ

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 29 - Definite Integration>JEE Main 17 March 2021 Shift 2>Q 35

Let

I_{n} = \int_{1}^{e} x^{19} (\log | x |)^{n} d x,

where

n \in N

. If

(20) I_{10} = α I_{9} + β I_{8},

for natural numbers

α

and

β

, then

α - β

equal to _______.