Definite Integration questions
424 published questions with worked solutions.
- The value of _ - /2 ^ /2 dx ^3 x + x is
- _0^ dx 1 + 3^ x is equal to
- If [y] = the greatest integer less than or equal to y then _ /2 ^ 3 /2 [2 x] ,dx is
- The value of _0^ 2 dx e^ x + 1 is
- _ a/4 ^ 3a/4 x a - x + x ,dx is equal to
- If f(x) = _0^ x ^ -1 t ,dt + _0^ x ^ -1 t ,dt, 0 < x < 2 , then f ! ( 4 ) is
- The value of _ ^ x|x| ,dx, where < 0 < , is
- _ -1 ^ 1 (x - [2x]) ,dx is equal to
- If f(x) = cases |x| + 1, & -1 x < 0 1 + |x|^2, & 0 x 1 cases then _ -1 ^ 1 f(x) ,dx is equal to
- Let f(x) = e^x + 1 e^x - 1 and _0^1 e^x + 1 e^x - 1 x ,dx = . Then _ -1 ^ 1 t f(t) ,dt is equal to
- Let f(x) be a continuous function in R such that f(x) + f(y) = f(x + y). If _0^3 f(x) ,dx = k then _ -3 ^ 3 f(x) ,dx is equal to
- Let f(x) be a continuous function such that f(x) does not vanish for all x R. If _2^3 f(x) ,dx= _ -2 ^3 f(x) ,dx then f(x), x R,...
- Let I= _ -a ^ a (p ^3x+q ^2x+r x) ,dx, where p,q,r are arbitrary constants. The numerical value of I depends on
- Let I_1= _0^1 e^ -x^2 dx, I_2= _0^1 e^ -x ^2x ,dx and I_3= _0^1 e^ -x^2 ^2x ,dx. Then
- If _ -2 ^ 3 f(x) ,dx=5 and _1^3 2-f(x) ,dx=6 then the value of _ -2 ^ 1 f(x) ,dx is
- Let f(x) be a continuous function such that _n^ n+1 f(x) ,dx=n^3, n Z. Then the value of _ -3 ^ 3 f(x) ,dx is
- If I= _0^1 x ,dx 8+x^3 then the smallest interval in which I lies is
- _ 1/2 ^ 2 ( e^x-1 e^x+1 )dx is equal to
- Let _0^a f(x) ,dx= and _0^a f(2a-x) ,dx= . Then _0^ 2a f(x) ,dx is equal to
- If f(-x)+f(x)=0 then _a^x f(t) ,dt is
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