Definite Integration questions
424 published questions with worked solutions.
- If f(a+b-x)=f(x) then _a^b xf(x) ,dx is equal to
- If A = _0^1 ^ -1 x ,dx and B = _0^1 ^ -1 x ,dx then 2 is equal to
- _ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n ^2 1 ] equals
- If _ x ^ 1 t^2 f(t) ,dt=1- x then f ! ( 1 3 ) is equal to
- The value of _ -2 ^ 0 x^3+3x^2+3x+3+(x+1) (x+1) ,dx is
- The value of _ - ^ ^2x 1+a^x ,dx, a>0 is
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- If f(x) and (x) are continuous functions in [0, 4] satisfying f(x) = f(4 - x), (x) + (4 - x) = 3 and _0^4 f(x) ,dx = 2 then the...
- _ 10 ^ 100 (x - [x]) ,dx is equal to _____.
- If f(x) = _a^x 1 f(x) ,dx (x > 0) and _a^1 1 f(x) ,dx = 2 then f(50) is _____.
- STATEMENT-1: _0^ /2 dx 1 + ^3 x = 4 . STATEMENT-2: _0^a f(x) ,dx = _0^a f(x + a) ,dx where f(x) is an integrable function.
- Let F(x) = _1^ x^2 t ,dt. STATEMENT-1: F'(x) = x. STATEMENT-2: If f(x) = _a^x (t) ,dt then f'(x) = (x).
- _ n 1n [n] e + [n] e^2 + [n] e^3 + + [n] e^n is equal to
- _0^a f(x) ,dx + _0^a f(2a - x) ,dx is equal to
- One or more may match with the same. Column I: (i) If f(x) is continuous in R and f(x) + f(x+1) = 1, where 0 x 1, then the value...
- If y = _0^ x^2 t , dt then dy dx is equal to
- Let f(x) be a periodic function of the period 1 and f ( 12 ) = 12. Let (x) = _0^x f(x + n) ,dx for all n N . Then ' ( 32 ) is...
- Let (x) = _0^x ^3 x ,dx. The function (x) is
- If _0^ x f( x) ,dx = A _0^ /2 f( x) ,dx then A is
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