antiderivative of an integral

[xc630]

Greetings i would appreciate some help with the following problem.

If f(X) = 15 -g(X) for -2 less then or equal to x is less than or equal to 2 (Trying to express -2 </= x </= 2), then the integral from -2 to 2 of [ f(x)-(g(x)] dx is?

I tried pluggin in 15- g(x) for f (x) leaving the integral from
-2 to 2 of 15- 2g (x) dx

from there I got 15x - g(x) ^2

I tried plugging in 2 and -2 leaving

[30 + (g(2)^2)] - [-30- (g(-2)^2)]

I gwould get 60 and then I'm not sure what to do with the rest if indeed this is correct. Some advice please!

 

[tkhunny]

1) Are you sure you have reported the entire problem? Given the right information, you may not need any antiderivative.

2) Remember the Chain Rule? (d/dx)(g(x))^2 = 2*g(x)*g`(x) -- You're not very close to that. You have g(x). The antiderivative of g(x) is not as you have stated it.