Home
Class 12
MATHS
If (d)/(dx)f(x)=g(x), find the value of ...

If `(d)/(dx)f(x)=g(x)`, find the value of `int_(a)^(b)f(x)g(x)dx`.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)[{f(b)}^(2)-{f(a)}^(2)]`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|61 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|58 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise MCQ EXERCISE 9A|15 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If (d)/(dx)f(x)=g(x) , then the value of int_(a)^(b)f(x)g(x)dx is -

If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), then find the value of int_(-3)^5g(x)dx .

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions f(x)=f(a-x) and g(x)+g(a-x)=a , then show that int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx . Hence find the value of int_(0)^(pi)xsinxdx .

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2) . Then the value of the integral int_(0)^(1) f(x)g(x) dx is equal to -

The value of (d)/(dx)5^(f(x)) is -

"If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))dx is equal to

Let f:[(1)/(2),1]to RR (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x)lt2f(x)" and "f((1)/(2))=1 Then the value of int_((1)/(2))^(1)f(x)dx lies in the interval

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

Evaluate: int[f(x)g''(x)-f ''(x)g(x)]dx

Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0 , If int_(1)^(4) (3)/(x) e^(sin x^(3))dx=F(k)-F(1) , then one of the possible value of k is -