Definite Integration questions
424 published questions with worked solutions.
- The value of 12 _0^3|x^2-3x+2|dx is _______.
- The value of 8 _0^ /2 ( x)^ 2023 ( x)^ 2023 +( x)^ 2023 dx is ____________.
- If _ 1/3 ^3| _ex|dx= m n _e ( n^2 e ), where m and n are coprime natural numbers, then m^2+n^2-5 is equal to __________.
- The value of the integral _ 1/2 ^2 ^ -1 x x dx is equal to
- _ n 3 n 4+ (2+ 1 n )^2+ (2+ 2 n )^2+ + (3- 1 n )^2 is equal to
- If (x) = 1 x _ /4 ^x(4 2 t-3 '(t))dt, x > 0, then ' ( 4 ) is equal to
- The value of _ /3 ^ /2 (2+3 x) x(1+ x) dx is equal to
- Let a differentiable function f satisfy f(x) + _3^xf(t) dt t = x+1 , x 3. Then 12f(8) is equal to :
- Let f be a non-negative function defined on the interval [0, 1]. If _0^x 1 - (f'(t))^2 ,dt = _0^xf(t) ,dt, 0 x 1, and f(0) = 0,...
- If I_n = _ - ^ nx (1 + ^x) x ,dx, n = 0, 1, 2, , then
- Let f : ℝ → ℝ be a continuous function which satisfies f(x) = _0^xf(t) ,dt. Then the value of f(ln 5) is
- _ n 1^p + 2^p + 3^p + + n^p n^ p+1 is
- _0^ 10 | x| ,dx is
- _0^ 2 [x^2 ]dx is
- _ n 1 + 2^4 + 3^4 + n^4 n^5 - _ n 1 + 2^3 + 3^3 + n^3 n^5
- If f(a + b - x) = f(x) then _a^b xf(x)dx is equal to
- _ n _ r=1 ^ n 1 n e^ r n is
- The value of _ -2 ^ 3 |1 - x^2 |dx is
- If _0^ xf( x)dx = A _0^ /2 f( x)dx, then A is
- If f(x) = e^x 1 + e^x , I_1 = _ f(-a) ^ f(a) xg x(1 - x) dx and I_2 = _ f(-a) ^ f(a) g x(1 - x) dx then the value of I_2 I_1 is
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