New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2023 · 11 Apr · Shift 2 · Q32

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 11 Apr · Shift 2 · Q32

Definite Integration question

2023 · 11 Apr · Shift 2 · Q32

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

f: \mathbb{R} \rightarrow \mathbb{R}

be a continuous function satisfying

\int_{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0

, then the value of

\alpha

is :

A
$-\sqrt{3}$
B
$\sqrt{2}$
C
$-\sqrt{2}$
D
$\sqrt{3}$

More from Definite Integration

Let the function $f : [0, 2] \to R$ be defined as $f (x) = {e^{m i n {x^{2}, x - [x]},} e^{[x - l o g_{e} x]}, x \in [0, 1) x \in [1, 2]$ where $[t]$ denotes the greatest…2023 · MCQ
If $\int_{- 0.15}^{0.15} 100 x^{2} - 1 d x = \frac{k}{3000}$ , then $k$ is equal to .2023 · Numerical
$\int_{0}^{\infty} \frac{6}{e ^{3 x} + 6 e ^{2 x} + 11 e ^{x} + 6} d x =$ 2023 · MCQ
Let for $x \in R, S_{0} (x) = x, S_{k} (x) = C_{k} x + k \int_{0}^{x} S_{k - 1} (t) d t$ , where $C_{0} = 1, C_{k} = 1 - \int_{0}^{1} S_{k - 1} (x) d x, k = 1, 2, 3, \dots$ Then $S_{2} (3) + 6 C_{3}$ is equal to .2023 · Numerical
The value of $\frac{e ^{- \frac{π}{4}} + 0 \int \frac{π}{4} e ^{- x} t a n ^{50} x d x}{0 \int \frac{π}{4} e ^{- x} ( t a n ^{49} x + t a n ^{51} x ) d x}$ is2023 · MCQ
Let $f_{n} = \int_{0}^{\frac{π}{2}} (\sum_{k = 1}^{n} sin^{k - 1} x) (\sum_{k = 1}^{n} (2 k - 1) sin^{k - 1} x) cos x d x, n \in N$ . Then $f_{21} - f_{20}$ is equal to 2023 · Numerical
If $0 \int 1 \frac{1}{( 5 + 2 x - 2 x ^{2} ) ( 1 + e ^{(2 - 4 x)} )} d x = \frac{1}{α} lo g_{e} (\frac{α + 1}{β}), α, β > 0$ , then $α^{4} - β^{4}$ is equal to :2023 · MCQ
The value of $12 0 \int 3 x^{2} - 3 x + 2 d x$ is 2023 · Numerical