How to find 5, 1 f(x)dx?

Question

If 7	f(x) dx = 14
1
and 7	f(x) dx = 3.3,
5
find 5	f(x) dx.
1

Answer 1

Given: ∫_{(from 1 to 7)} f(x)dx = 14 and ∫_{(from 5 to 7)}f(x)dx = 3.3

So, ∫_{(from 1 to 5)}f(x)dx = ∫_{(from 1 to 7)}f(x)dx + ∫_{(from 7 to 5)}f(x)dx = 14 - ∫_{(from 5 to 7)}f(x)dx = 14 - 3.3 = 10.7