JEE Main Mathematics — Definite Integration Previous-Year Questions

Let A = bmatrix 1 & 3 & -1 \ 2 & 1 & α \ 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ∫₀^x (t² + 2t + 3) dt, x […

The value of the integral ∫₀² √(x(x²+x+1))(√(x+1))(√(x⁴+x²+1)) dx is equal to:

Let a differentiable function f satisfy the equation ∫₀³⁶ f ((t x)/(36) ) d t=4 α f(x). If y=f(x) is a standard parabol…

6 ∫₀ⁱ|( 3 x+ 2 x+ x)| d x is equal to \\\\_.

Let ∫₋₂² (| x| + [x x]) dx = 2(3 - 2) + β, where [·] is the greatest integer function. Then β ((β)/(2) ) equals:

The value of the integral ∫π/₆ⁱ/³ ((4 - ² x)/(⁴ x) ) dx is:

Let f be a twice differentiable function such that f(x)=∫₀x(t-x)dt-∫₀xf(t) t dt, x (-(π)/(2),(π)/(2) ). Then f'' ((π)/(…

The value of the integral ∫₋₁¹ ((x³ + |x| + 1)/(x² + 2|x| + 1) ) dx is equal to :

Let [·] denote the greatest integer function. Then the value of ∫₀³ (e^x + e⁻x[x]! ) dx is :

Let (2¹⁻a + 2¹⁺a), f(a), (3^a + 3⁻a) be in A.P. and α be the minimum value of f(a). Then the value of the integral ∫₍α₋…