New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2022 · 25 Jul · Shift 1 · Q29

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 25 Jul · Shift 1 · Q29

Definite Integration question

2022 · 25 Jul · Shift 1 · Q29

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

For any real number

x

, let

[x]

denote the largest integer less than equal to

x

. Let

f

be a real valued function defined on the interval

[-10,10]

by

f(x)=\left\{\begin{array}{l}x-[x], \text { if }[x] \text { is odd } \\ 1+[x]-x, \text { if }[x] \text { is even } .\end{array}\right.

Then the value of

\frac{\pi^{2}}{10} \int_{-10}^{10} f(x) \cos \pi x \,d x

is :

A
4
B
2
C
1
D
0

More from Definite Integration

Let $[t]$ denote the greatest integer less than or equal to $t$ . Then the value of the integral $\int_{- 3}^{101} ([sin (π x)] + e^{[c o s (2 π x)]}) d x$ is equal to2022 · MCQ
Let $f$ be a twice differentiable function on $R$ . If $f^{'} (0) = 4$ and $f (x) + 0 \int x (x - t) f^{'} (t) d t = (e^{2 x} + e^{- 2 x}) cos 2 x + \frac{2}{a} x$ , then $(2 a + 1)^{5} a^{2}$ is equal to …2022 · Numerical
Let $a_{n} = - 1 \int n (1 + \frac{x}{2} + \frac{x ^{2}}{3} + ..... + \frac{x ^{n - 1}}{n}) d x$ for every n $\in$ N. Then the sum of all the elements of the set {n} $\in$ N : an $\in$ (2, 30)} is …2022 · Numerical
The value of $0 \int π \frac{e ^{c o s x} s i n x}{( 1 + c o s ^{2} x ) ( e ^{c o s x} + e ^{- c o s x} )} d x$ is equal to:2022 · MCQ
If $b_{n} = \int_{0}^{\frac{π}{2}} \frac{c o s ^{2} n x}{s i n x} d x, n \in N$ , then2022 · MCQ
The value of b > 3 for which $12 3 \int b \frac{1}{( x ^{2} - 1 ) ( x ^{2} - 4 )} d x = lo g_{e} (\frac{49}{40})$ , is equal to .2022 · Numerical
If $n (2 n + 1) \int_{0}^{1} (1 - x^{n})^{2 n} d x = 1177 \int_{0}^{1} (1 - x^{n})^{2 n + 1} d x$ , then $n \in N$ is equal to …2022 · Numerical
$0 \int 20 π (∣ sin x ∣ + ∣ cos x ∣)^{2} d x is equal to$ 2022 · MCQ