Definite Integration questions
424 published questions with worked solutions.
- If _ - /2 ^ /2 96x^2 ^2 x (1+e^x) dx = ( ^2 + ), , Z, then ( + )^2 equals :
- Let for some function y = f(x), _0^x t f(t) ,dt = x^2 f(x), x > 0 and f(2) = 3. Then f(6) is equal to
- Let f be a real valued continuous function defined on the positive real axis such that g(x)= _0^x tf(t)dt. If g(x^3)=x^6+x^7,...
- Let f : (0, ) R be a twice differentiable function. If for some a 0, _0^1 f( x)d = af(x), f(1) = 1 and f(16) = 1 8 , then 16 - f'...
- Let f(x) = _0^x t(t^2-9t+20) ,dt, 1 x 5. If the range of f is [ , ], then 4( + ) equals :
- If 24 _0^ /4 ( | (4x- 12 ) |+[2 x] )dx = 2 + , where [.] denotes the greatest integer function, then is equal to _____.
- Let (a, b) be the point of intersection of the curve x^2 = 2y and the straight line y - 2x - 6 = 0 in the second quadrant. Then...
- Let f : [1, ) [2, ) be a differentiable function. If 10 _1^x f(t) ,dt = 5xf(x) - x^5 - 9 for all x 1, then the value of f(3) is :
- The integral _0^ 8x ,dx 4 ^2 x + ^2 x is equal to
- The value of _ -1 ^ 1 (1+ |x|-x )e^x + ( |x|-x )e^ -x e^x+e^ -x dx is equal to
- Let f(x) be a positive function and I_1 = _ - 1 2 ^ 1 2xf(2x(1-2x))dx and I_2 = _ -1 ^ 2 f(x(1-x))dx. Then the value of I_2 I_1...
- Let f(x) + 2f ( 1 x ) = x^2 + 5 and 2g(x) - 3g ( 1 x ) = x, x > 0. If = _1^2 f(x)dx, and = _1^2 g(x)dx, then the value of 9 + is :
- The value of _ - /2 ^ /2 ^2 x 1 + 2^x ,dx is :
- If f(x) = _0^x t( x - t) ,dt then
- If f(x) = 2 - x x 2 + x x and g(x) = _e x, (x > 0) then the value of the integral _ - /4 ^ /4 g(f(x)) ,dx is:
- Let f(x) = _0^x g(t) ,dt, where g is a non-zero even function. If f(x + 5) = g(x), then _0^x f(t) ,dt equals:
- The value of _0^ /2 ^3x x + x dx is:
- The value of the integral _ - /2 ^ /2 ^4 x (1 + ( 2 + x 2 - x ) )dx is
- The value of integral _ /4 ^ 3 /4 x 1 + x ,dx is -
- If I_1 = _0^1 e^ -x ^2 x ,dx; I_2 = _0^1 e^ -x^2 ^2 x ,dx and I_3 = _0^1 e^ -x^3 ,dx; then -
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