Definite Integration questions
424 published questions with worked solutions.
- Let S_n = _ k=1 ^ n n n^2+kn+k^2 T_n = _ k=0 ^ n-1 n n^2+kn+k^2 , for n = 1, 2, 3, . Then,
- Statement-I : The value of the integral _ /6 ^ /3 dx 1+ x is equal to 6 . Statement-II : _a^b f(x)dx = _a^b f(a+b-x)dx.
- The value of _ - /6 ^ /6 ( + 4x^ 11 1 - (|x| + /6) )dx is equal to
- 6 _0^ |( 3x + 2x + x)| ,dx is equal to _____
- Let [.] denote the greatest integer function and f(x) = _ n 1 n^3 _ k=1 ^ n [ k^2 3^x ]. Then 12 _ j=1 ^ f(j) is equal to _____.
- If _0^1 4 ^ -1 (1 - 2x + 4x^2) , dx = a ^ -1 (2) - b _e(5), where a, b N, then (2a + b) is equal to _____.
- Let f : [1, ) R be a differentiable function. If 6 _1^x f(t) ,dt = 3xf(x) + x^3 - 4 for all x 1, then the value of f(2) - f(3) is
- The value of _ - /2 ^ /2 ( 1 [x]+4 )dx, where [ ] denotes the greatest integer function, is
- Let [ ] be the greatest integer function. If = _0^ 64 (x^ 1/3 -[x^ 1/3 ] )dx, then 1 _0^ ( ^2 ^6 + ^6 )d is equal to ____ .
- The value of the integral _ /24 ^ 5 /24 dx 1+ [3] 2x is :
- Let f be a twice differentiable non-negative function such that (f(x))^2 = 25 + _0^x ((f(t))^2+(f'(t))^2 )dt. Then the mean of f(...
- The number of elements in the set S = x : x [0,100] and _0^x t^2 (x-t) ,dt = x^2 is.....
- Let f be a polynomial function such that f(x^2+1) = x^4+5x^2+2, for all x R. Then _0^3 f(x)dx is equal to
- The value of _ r=1 ^ 20 ( ( _0^r x| x|dx ) ) is _____.
- Let [.] denote the greatest integer function. Then _ - /2 ^ /2 ( 12(3+[x]) 3+[ x]+[ x] )dx is equal to:
- Let for ƒ(x) = 7tan⁸x + 7tan⁶x – 3tan⁴x – 3tan²x, I_1 = _0^ /4 f(x)dx and I_2 = _0^ /4 xf(x)dx. Then 7I1 + 12I2 is equal to :
- If I = _0^ /2 ^ 3/2 x ^ 3/2 x + ^ 3/2 x dx, then _0^ 2I x x x ^4 x + ^4 x dx, equals :
- The value of _ e^2 ^ e^4 1 x ( e^ (( _e x)^2+1)^ -1 e^ (( _e x)^2+1)^ -1 +e^ ((6- _e x)^2+1)^ -1 )dx is-
- In I(m, n) = _0^1 x^ m-1 (1-x)^ n-1 dx, m, n > 0, then I(9, 14) + I(10, 13) is
- Let f be a differentiable function such that 2(x + 2)^2 f(x) - 3(x + 2)^2 = 10 _0^x (t+2)f(t) , dt, x 0. Then f(2) is equal to...
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