Definite Integration questions
424 published questions with worked solutions.
- _ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + + 1 n^2 ^21 ] equals
- Let f : R R be a differentiable function having f(2) = 6, f'(2) = ( 1 48 ). Then _ x 2 _6^ f(x) 4t^3 x-2 dt equals
- The value of _ - ^ ^2x 1 + a^x dx, a > 0, is
- The value of the integral, _3^6 x 9 - x + x dx is
- _0^ xf( x)dx is equal to
- _ -3 /2 ^ - /2 [(x + )^3 + ^2(x + 3 ) ]dx is equal to
- The value of _1^a[x]f'(x)dx, a > 1, where [x] denotes the greatest integer not exceeding x is
- Let F(x) = f(x) + f ( 1x ), where f(x) = _1^x t 1 + t dt. Then F(e) equals
- _0^ [ x]dx, [•] denotes the greatest integer function, is equal to
- Let p(x) be a function defined on R such that p'(x) = p'(1 - x), for all x [0, 1], p(0) = 1 and p(1) = 41. Then _0^1p(x)dx equals
- The value of _0^1 8 (1 + x) 1 + x^2 dx is
- The value of I= _ _e 2 ^ _e 3 x x^2 x^2+ ( _e 6-x^2) dx is
- The value of the integral _ - /2 ^ /2 (x^2+ -x +x ) x ,dx is equal to
- The integral _ -1/2 ^ 1/2 ([x]+ _e ( 1+x 1-x ) )dx, where [x] represents greatest integer function, equals
- _ -1 ^ 1 ( 2-x 2+x )dx=
- _ - 2 ^ 2 f(x)dx= Where f(x)= |x|+ |x|, x [- 2 , 2 ]
- _0^1 x(1-x)^n ,dx =
- _0^ 2 ( x + | x|) ,dx =
- If _ a ^ b x^ 3 dx=0 and _ a ^ b x^ 2 dx= 2 3 , then a and b are respectively______
- The value of _0^ /2 dx 1+ ^3 x is
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