Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 33

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

If $f (x)$ is a function satisfying $f (\frac{1}{x}) + x^{2} f (x) = 0$ for all $x (x \neq 0),$ then the value of $\int_{\tan θ}^{\cot θ} f (x) d x$ is

50% studentsanswered this correctly

Important Questions on Definite Integrals

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 34

\int_{0}^{1} \frac{\log (1 - x)}{x} d x

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 35

\int_{0}^{1} \frac{\log x}{1 + x} d x

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 36

The value of

\int_{0}^{1} |x \cos π x| d x

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 37

If

A = \int_{1}^{\sin θ} \frac{t}{1 + t^{2}} d t

and

B = \int_{1}^{cosec θ} \frac{d t}{t (1 + t^{2})},

then the value of

|\begin{matrix} A & A^{2} & B \\ e^{A} e^{B} & B^{2} & - 1 \\ 1 & A^{2} + B^{2} & - 1 \end{matrix}|

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 38

If

\int_{a}^{b} {(x - a)}^{3} {(b - x)}^{4} d x = \frac{{(b - a)}^{m}}{n},

then

(m, n)

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 39

If

f (x)

is a periodic function of period

a

, then

\int_{0}^{n a} f (x) d x

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 40

\int_{0}^{3} \{\sqrt{x}\} d x,

where

\{x\}

denotes the fractional part of

x,

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 10 - Definite Integrals>Target Exercises>Q 41

If

I_{1} = \int_{0}^{a} [x] d x

and

I_{2} = \int_{0}^{a} \{x\} d x,

where

[x]

and

\{x\}

denote respectively, the integral and fractional parts of

x

and

a

is a positive integer, then