Definite Integration questions
424 published questions with worked solutions.
- If f(x) and g(x) be continuous functions over the closed interval [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2. Then _0^a f(x)...
- If f(x)=f(a+x) and _0^a f(x) ,dx=p then _a^ na f(x) ,dx is equal to
- Let f(x) be a given integrable function such that f(x+k)=f(x) for all x R. Then _a^ a+k f(x) ,dx depends for its value on
- The value of _ /4 ^ 3 /4 x 1+ x ,dx is equal to
- The value of _0^ /2 dx 1+ ^3x is
- Let f and g be two continuous functions. Then _ - /2 ^ /2 f(x)+f(-x) g(x)-g(-x) ,dx is equal to
- Let _a^b f(x) ,dx=p and _a^b|f(x)| ,dx=q. Then
- If f(x)= _0^x (1+t^2) ,dt then the value of f''(1) is equal to
- If f(x)= _x^ x^2 dt 1+t^3 then f'(2) is equal to
- If f(2a-x)=f(x) and _0^a f(x) ,dx= then _0^ 2a f(x) ,dx is
- If y= _0^x x ,dx then the value of dy dx at x= 2 is
- If y= _x^ x^2 5-t^2 ,dt then the value of dy dx at x= 2 is
- If A= _0^ x x+ x ,dx, B= _0^ x x- x ,dx then
- Let f(a)>0, and let f(x) be a nondecreasing continuous function in [a,b]. Then 1 b-a _a^b f(x) ,dx has the
- The value of _0^ nx x ,dx, n N, is
- If f(x)= _x^ x^2 dt ( t)^2 , x 0, x 1, then f(x) is
- Let f(x)= _0^x|x-1| ,dx, x 0. Then f'(x) is
- If _ a-n ^ n e^ x(a-x) ,dx= then the value of _ a-n ^ n x ,e^ x(a-x) ,dx, a 2n, is
- Let f(x)= x,1-x for all x R. Then the value of _0^ 2 f(x) ,dx is
- If I = _ 1/ ^ 1x (x - 1x )dx then I is equal to
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