# Thread: Finding a definite integral from other given definite integrals.

1. ## Finding a definite integral from other given definite integrals.

What is this technique called?:

Suppose f is continuous and $\displaystyle \displaystyle \int_{-2}^{2}f(x)dx = 4$ and
$\displaystyle \displaystyle \int_{-2}^{5}g(x)dx = 2$

Determine $\displaystyle \displaystyle \int_{5}^{2}f(y)dy$

I am just doing this out of memory, tell me if its right
$\displaystyle \displaystyle \int_{5}^{2}f(y)dy = -(\int_{-2}^{5}g(x)dx) - (-(\int_{-2}^{2}f(x)dx))$
$\displaystyle \displaystyle \int_{5}^{2}f(y)dy = - 2 - (-4) = 2$

2. I don't think it would have a name. It isn't that significant.

3. no name? is my calculation atleast correct?

4. Originally Posted by bijosn
no name? is my calculation atleast correct?
Assuming it's meant to be f and not g in the second given integral, your answer is correct. (If it was wrong the TheCoffeeMachine would have said so in his/her post, by the way).

5. thank you, I apologize for not being sufficiently intuitive to understand the subtle ways of the coffee machine