New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2023 · 6 Apr · Shift 1 · Q29

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 6 Apr · Shift 1 · Q29

Definite Integration question

2023 · 6 Apr · Shift 1 · Q29

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

5 f(x)+4 f\left(\frac{1}{x}\right)=\frac{1}{x}+3, x \gt 0

. Then

18 \int_{1}^{2} f(x) d x

is equal to :

A
$10 \log _{\mathrm{e}} 2+6$
B
$5 \log _{e} 2-3$
C
$10 \log _{\mathrm{e}} 2-6$
D
$5 \log _{\mathrm{e}} 2+3$

More from Definite Integration

Let $f (x)$ be a function satisfying $f (x) + f (π - x) = π^{2}, \forall x \in R$ . Then $\int_{0}^{π} f (x) sin x d x$ is equal to :2023 · MCQ
$lim_{n \to \infty} {(2^{\frac{1}{2}} - 2^{\frac{1}{3}}) (2^{\frac{1}{2}} - 2^{\frac{1}{5}}) \dots .. (2^{\frac{1}{2}} - 2^{\frac{1}{2 n + 1}})}$ is equal to :2023 · MCQ
Let $[t]$ denote the greatest integer $\leq t$ . Then $\frac{2}{π} \int_{π /6}^{5 π /6} (8 [cosec x] - 5 [cot x]) d x$ is equal to .2023 · Numerical
Let $[t]$ denote the greatest integer function. If $\int_{0}^{2.4} [x^{2}] d x = α + β 2 + γ 3 + δ 5$ , then $α + β + γ + δ$ is equal to .2023 · Numerical
Let $f$ be a continuous function satisfying $\int_{0}^{t^{2}} (f (x) + x^{2}) d x = \frac{4}{3} t^{3}, \forall t > 0$ . Then $f (\frac{π ^{2}}{4})$ is equal to :2023 · MCQ
The value of the integral $\int_{- l o g_{e} 2}^{l o g_{e} 2} e^{x} (lo g_{e} (e^{x} + 1 + e^{2 x})) d x$ is equal to :2023 · MCQ
For $m, n > 0$ , let $α (m, n) = \int_{0}^{2} t^{m} (1 + 3 t)^{n} d t$ . If $11 α (10, 6) + 18 α (11, 5) = p (14)^{6}$ , then $p$ is equal to .2023 · Numerical
If $f : R \to R$ be a continuous function satisfying $\int_{0}^{\frac{π}{2}} f (sin 2 x) sin x d x + α \int_{0}^{\frac{π}{4}} f (cos 2 x) cos x d x = 0$ , then the value of $α$ is :2023 · MCQ