New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2024 · 5 Apr · Shift 1 · Q46

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 5 Apr · Shift 1 · Q46

Definite Integration question

2024 · 5 Apr · Shift 1 · Q46

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of

\int_{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y

is :

A
$\frac{\pi}{2}$
B
$\pi^2$
C
$\frac{\pi^2}{2}$
D
$2 \pi^2$

More from Definite Integration

Let $β (m, n) = 0 \int 1 x^{m - 1} (1 - x)^{n - 1} d x, m, n > 0$ . If $0 \int 1 (1 - x^{10})^{20} d x = a \times β (b, c)$ …2024 · MCQ
If $f (t) = 0 \int π \frac{2 x d x}{1 - c o s ^{2} t s i n ^{2} x}, 0 < t < π$ , then the value of $0 \int \frac{π}{2} \frac{π ^{2} dt}{f ( t )}$ equals .2024 · Numerical
$0 \int π /4 \frac{c o s ^{2} x s i n ^{2} x}{( c o s ^{3} x + s i n ^{3} x ) ^{2}} d x$ is equal to2024 · MCQ
Let $r_{k} = \frac{\int _{0}^{1} ( 1 - x ^{7} ) ^{k} d x}{\int _{0}^{1} ( 1 - x ^{7} ) ^{k + 1} d x}, k \in N$ . Then the value of $\sum_{k = 1}^{10} \frac{1}{7 ( r _{k} - 1 )}$ is equal to .2024 · Numerical
Let $[t]$ denote the largest integer less than or equal to $t$ . If $0 \int 3 ([x^{2}] + [\frac{x ^{2}}{2}]) d x = a + b 2 - 3 - 5 + c 6 - 7$ , where $a, b, c \in Z$ …2024 · Numerical
The value of $k \in N$ for which the integral $I_{n} = \int_{0}^{1} (1 - x^{k})^{n} d x, n \in N$ , satisfies $147 I_{20} = 148 I_{21}$ is2024 · MCQ
Let $α \int l o g_{e} 4 \frac{d x}{e ^{x} - 1} = \frac{π}{6}$ . Then $e^{α}$ and $e^{- α}$ are the roots of the equation :2024 · MCQ
Let $lim_{n \to \infty} (\frac{n}{n ^{4} + 1} - \frac{2 n}{( n ^{2} + 1 ) n ^{4} + 1} + \frac{n}{n ^{4} + 16} - \frac{8 n}{( n ^{2} + 4 ) n ^{4} + 16} + \dots + \frac{n}{n ^{4} + n ^{4}} - \frac{2 n \cdot n ^{2}}{( n ^{2} + n ^{2} ) n ^{4} + n ^{4}})$ …2024 · Numerical