New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2024 · 1 Feb · Shift 1 · Q58

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 1 Feb · Shift 1 · Q58

Definite Integration question

2024 · 1 Feb · Shift 1 · Q58

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

\int\limits_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \mathrm{~d} x}{\left(1+\mathrm{e}^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _{\mathrm{e}}(3+2 \sqrt{2})

, where

\alpha, \beta

are integers, then

\alpha^2+\beta^2

equals :

Numerical answer

More from Definite Integration

If $0 \int \frac{π}{3} cos^{4} x d x = a π + b 3$ , where $a$ and $b$ are rational numbers, then $9 a + 8 b$ is equal to :2024 · MCQ
The value of $0 \int 1 (2 x^{3} - 3 x^{2} - x + 1)^{\frac{1}{3}} d x$ is equal to :2024 · MCQ
Let $f : (0, \infty) \to R$ and $F (x) = 0 \int x t f (t) dt$ . If $F (x^{2}) = x^{4} + x^{5}$ , then $r = 1 \sum 12 f (r^{2})$ is equal to …2024 · Numerical
$Let f (x) = {- 2, x - 2, - 2 \leq x \leq 0 0 < x \leq 2 and h (x) = f (∣ x ∣) + ∣ f (x) ∣ . Then \int_{- 2}^{2} h (x) d x is equal to:$ …2024 · MCQ
If the shortest distance between the lines $\frac{x + 2}{2} = \frac{y + 3}{3} = \frac{z - 5}{4}$ and $\frac{x - 3}{1} = \frac{y - 2}{- 3} = \frac{z + 4}{2}$ is $\frac{38}{3 5} k$ , and $0 \int k [x^{2}] d x = α - α$ …2024 · Numerical
If $\int_{0}^{\frac{π}{4}} \frac{s i n ^{2} x}{1 + s i n x c o s x} d x = \frac{1}{a} lo g_{e} (\frac{a}{3}) + \frac{π}{b 3}$ , where $a, b \in N$ , then $a + b$ …2024 · Numerical
Let $f (x) = \int_{0}^{x} (t + sin (1 - e^{t})) d t, x \in R$ . Then, $lim_{x \to 0} \frac{f ( x )}{x ^{3}}$ is equal to2024 · MCQ
If the value of the integral $- 1 \int 1 \frac{c o s α x}{1 + 3 ^{x}} d x$ is $\frac{2}{π}$ .Then, a value of $α$ is2024 · MCQ