JEE Main 2025 — Definite Integration Questions with Solutions

IfI(m, n)=∫₀¹ xm⁻¹(1-x)ⁿ⁻¹ d x, m, n0, then I(9,14)+I(10,13) is

Let f(x)=∫₀^t t (t²-9 t+20 ) d t, 1 ≤ x ≤ 5. If the range of f is [α, β], then 4(α+β) equals :

Let for some function y=f(x), ∫₀^x t f(t) d t=x² f(x), x0 and f(2)=3. Then f(6) is equal to

If ∫₋₍π₎/₍₂₎⁽ⁱ⁾/⁽²⁾ (96 x² ² x)/( (1+e^x )) d x=π (α π²+β ), α, β Z, then (α+β)² equals

The value of ∫₋₁¹ (1+√(|x|-x)) e^x+(√(|x|-x)) e⁻xe^x+e⁻x d x is equal to

The integral ∫₀^π (8 x d x)/(4 ² x+ ² x) is equal to

Let f:(0, ∞) → R be a twice differentiable function. If for some a ≠ 0, ∫₀¹ f(λ x) d λ=a f(x), f(1)=1 and f(16)=(1)/(8)…

Let f be a real valued continuous function defined on the positive real axis such that g(x)=∫₀^x t f(t) dt. If g (x³ )=…

Let the domain of the function f(x)= ₂ ₄ ₆ (3+4 x-x² ) be (a, ~b). If ∫₀b⁻a [x² ] dx=p-q-r, p, q, r N, gcd(p, q, r)=1,…

If I=∫₀⁽ⁱ⁾/⁽²⁾ ⁽³⁾/⁽²⁾ x ⁽³⁾/⁽²⁾ x+ ⁽³⁾/⁽²⁾ x ~d x, then ∫₀²¹ (x x x)/( ⁴ x+ ⁴ x) ~d x equals :