New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2025 · 2 Apr · Shift 1 · Q50

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 2 Apr · Shift 1 · Q50

Definite Integration question

2025 · 2 Apr · Shift 1 · Q50

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let [.] denote the greatest integer function. If

\int\limits_0^{e^3}\left[\frac{1}{e^{x-1}}\right] d x=\alpha-\log _e 2

, then

\alpha^3

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Definite Integration

Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10 \int_{1}^{1} f (t) dt = 5 x f (x) - x^{5} - 9$ for all $x ⩾ 1$ , then the value of $f (3)$ is :2025 · MCQ
Let $x^{2} = 2 y$ be the point of intersection of the curve $x^{2} = 2 y$ and the straight line $y - 2 x - 6 = 0$ in the second quadrant. Then the integral $I = \int_{a}^{b} \frac{9 x ^{2}}{1 + 5 ^{x}} d x$ is equal to :2025 · MCQ
$4 \int_{0}^{1} (\frac{1}{3 + x ^{2} + 1 + x ^{2}}) d x - 3 lo g_{e} (3)$ is equal to :2025 · MCQ
Let the domain of the function $f (x) = lo g_{2} lo g_{4} lo g_{6} (3 + 4 x - x^{2})$ be $\int_{0}^{b - a} [x^{2}] d x = p - q - r, p, q, r \in N, gcd (p, q, r) = 1$ . If $\int_{0}^{b - a} [x^{2}] d x = p - q - r, p, q, r \in N, gcd (p, q, r) = 1$ , where $[\cdot]$ is the…2025 · MCQ
The integral $\int_{0}^{π} \frac{8 x d x}{4 c o s ^{2} x + s i n ^{2} x}$ is equal to2025 · MCQ
The value of $\int_{- 1}^{1} \frac{( 1 + ∣ x ∣ - x ) e ^{x} + ( ∣ x ∣ - x ) e ^{- x}}{e ^{x} + e ^{- x}} d x$ is equal to2025 · MCQ
Let $f (x) + 2 f (\frac{1}{x}) = x^{2} + 5$ and $2 g (x) - 3 g (\frac{1}{2}) = x, x > 0$ . If $α = \int_{1}^{2} f (x) d x$ , and $β = \int_{1}^{2} g (x) d x$ , then the value of $9 α + β$ is :2025 · MCQ
The integral $\int_{0}^{π} \frac{( x + 3 ) s i n x}{1 + 3 c o s ^{2} x} d x$ is equal to2025 · MCQ