New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2023 · 31 Jan · Shift 2 · Q33

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 31 Jan · Shift 2 · Q33

Definite Integration question

2023 · 31 Jan · Shift 2 · Q33

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x\gt 0

, then

\emptyset^{\prime}\left(\frac{\pi}{4}\right)

is equal to :

A
$\frac{4}{6+\sqrt{\pi}}$
B
$\frac{4}{6-\sqrt{\pi}}$
C
$\frac{8}{\sqrt{\pi}}$
D
$\frac{8}{6+\sqrt{\pi}}$

More from Definite Integration

Let $f (θ) = sin θ + - π /2 \int π /2 (sin θ + t cos θ) f (t) d t$ . Then the value of $\int_{0}^{π /2} f (θ) d θ$ is .2022 · Numerical
Let $0 \leq x \leq 2 M a x {\frac{9 - x ^{2}}{5 - x}} = α$ and $0 \leq x \leq 2 M in {\frac{9 - x ^{2}}{5 - x}} = β$ . If $β - \frac{8}{3} \int 2 α - 1 M a x {\frac{9 - x ^{2}}{5 - x}, x} d x = α_{1} + α_{2} lo g_{e} (\frac{8}{15})$ …2022 · Numerical
The value of the integral $- π /2 \int π /2 \frac{d x}{( 1 + e ^{x} ) ( s i n ^{6} x + c o s ^{6} x )}$ is equal to2022 · MCQ
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 $f (x) = {x - [x], if [x] is odd 1 + [x] - x, if [x] is even .$ …2022 · MCQ
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