Question

Given that ∫61f(x)dx=1,∫63f(x)dx=6 and ∫71f(x)dx=7 find ∫73f(x)dx.

Answer 1

∫f(6)-∫f(1) = 1, ∫f(6)-∫f(3)=6, and ∫f(7)-∫f(1)=7. Changing around the first and third equation, we can get ∫f(1)=∫f(6)-1, and ∫f(1)=∫f(7)-7. Then we get that ∫f(6)-1=∫f(7)-7, and that ∫f(6)=∫f(7)-6. Then plug into the second equation, to get ∫f(7)-6-∫f(3)=6 or ∫f(7)-∫f(3)=12. So ∫73f(x)dx = 12.