New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2023 · 29 Jan · Shift 2 · Q34

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 29 Jan · Shift 2 · Q34

Definite Integration question

2023 · 29 Jan · Shift 2 · Q34

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of the integral

\int_1^2 {\left( {{{{t^4} + 1} \over {{t^6} + 1}}} \right)dt}

is

A
${\tan ^{ - 1}}{1 \over 2} - {1 \over 3}{\tan ^{ - 1}}8 + {\pi \over 3}$
B
${\tan ^{ - 1}}2 - {1 \over 3}{\tan ^{ - 1}}8 + {\pi \over 3}$
C
${\tan ^{ - 1}}2 + {1 \over 3}{\tan ^{ - 1}}8 - {\pi \over 3}$
D
${\tan ^{ - 1}}{1 \over 2} + {1 \over 3}{\tan ^{ - 1}}8 - {\pi \over 3}$

More from Definite Integration

The value of the integral $1/2 \int 2 \frac{t a n ^{- 1} x}{x} d x$ is equal to :2023 · MCQ
If [t] denotes the greatest integer $\leq t$ , then the value of $\frac{3 ( e - 1 )}{e} 1 \int 2 x^{2} e^{[x] + [x^{3}]} d x$ is :2023 · MCQ
$lim_{x \to 0} \frac{48}{x ^{4}} \int_{0}^{x} \frac{t ^{3}}{t ^{6} + 1} d t$ is equal to .2023 · Numerical
Let $α \in (0, 1)$ and $β = lo g_{e} (1 - α)$ . Let $P_{n} (x) = x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3} + ... + \frac{x ^{n}}{n}, x \in (0, 1)$ . Then the integral $0 \int α \frac{t ^{50}}{1 - t} d t$ …2023 · MCQ
The value of $\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{( 2 + 3 s i n x )}{s i n x ( 1 + c o s x )} d x$ is equal to :2023 · MCQ
Let $α > 0$ . If $0 \int α \frac{x}{x + α - x} d x = \frac{16 + 20 2}{15}$ , then $α$ is equal to :2023 · MCQ
If $ϕ (x) = \frac{1}{x} \frac{π}{4} \int x (42 sin t - 3 ϕ^{'} (t)) d t, x > 0$ , then $\emptyset^{'} (\frac{π}{4})$ is equal to :2023 · MCQ
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