New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2025 · 29 Jan · Shift 2 · Q46

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 29 Jan · Shift 2 · Q46

Definite Integration question

2025 · 29 Jan · Shift 2 · Q46

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

24 \int\limits_0^{\frac{\pi}{4}} \bigg[\sin \left| 4x - \frac{\pi}{12} \right| + [2 \sin x] \bigg] dx = 2\pi + \alpha

, where

[\cdot]

denotes the greatest integer function, then

\alpha

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Definite Integration

If $t \to 0 lim (0 \int 1 (3 x + 5)^{t} d x)^{\frac{1}{t}} = \frac{α}{5 e} (\frac{8}{5})^{\frac{2}{3}}$ , then $α$ is equal to .2025 · Numerical
The value of the integral $0 \int π /4 \frac{x d x}{s i n ^{4} ( 2 x ) + c o s ^{4} ( 2 x )}$ equals :2024 · MCQ
If $- π /2 \int π /2 \frac{8 2 c o s x d x}{( 1 + e ^{s i n x} ) ( 1 + s i n ^{4} x )} = α π + β lo g_{e} (3 + 22)$ , where $α, β$ are integers, then $α^{2} + β^{2}$ …2024 · Numerical
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