How do I find the integral of like four integrals that are combined?

Question

anonymous · Answer

$$\int\limits_{a}^{b}f(x)dx=13, \int\limits_{a}^{b}(f(x))^2dx=8, \int\limits_{a}^{b} g(t)dt=7, and \int\limits_{a}^{b} (g(t))^2dt=10$$

anonymous · Answer

Given that find the integral $$\int\limits_{a}^{b}(f(x))^2-(g(x))^2)dx$$

campbell_st · Answer

well it may be a typo by your integrals are involving different variables.... one x and one t. 

but your problem can be written as, using some of the basic rules of integrals 

$$\int\limits_{a}^{b}( f(x))^2 dx - \int\limits_{a}^{b} (g(x))^2 dx$$

now you can substitute the values and get 

8 - 10  = -2

anonymous · Answer

so -2 is the answer?

anonymous · Answer

Ohhhh okay I get it! Thank you!!! :)

campbell_st · Answer

glad to help