Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 2

MEDIUM

JEE Advanced

IMPORTANT

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$\int_{0}^{3} [x] d x$ where, $[\cdot]$ denotes greatest integer function, is equal to

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Important Questions on Definite Integrals

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 3

\int_{0}^{1.5} [x^{2}] d x

is equal to, where

[\cdot]

represents the greatest integer function

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 4

\int_{0}^{2} |x^{2} + 2 x - 3| d x

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 5

For any real number

x,

the value of

\int_{0}^{x} [x] d x

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 6

The value of

\int_{\frac{π}{6}}^{\frac{5 π}{6}} \sqrt{4 - 4 \sin^{2} t} d t

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 7

If for a real number

y, [y]

is the greatest integer less than or equal to

y,

then the value of the integral

\int_{\frac{π}{2}}^{\frac{3 π}{2}} [2 \sin x] d x,

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 8

The value of

\int_{0}^{\frac{π}{2}} (2 logsin x - logsin 2 x) d x

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 9

The value of

\int_{0}^{\frac{π}{2 n}} \frac{1}{1 + \cot n x} d x

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Work Book Exercise 10.2>Q 10

The value of

\int_{0}^{\frac{32 π}{3}} \sqrt{1 + \cos 2 x} d x

is