Question

If the integral from 0 to 3 of f(x)dx=6 and the integral from 3 to 5 of f(x)=4, then the integral of 5 to 0 of (3+2f(x))dx= ...
The answer is 35.
Please help how to get to this answer.

Answer 1

\[
\int\limits_5^03+2f(x)\;dx = 3\int\limits_5^0\;dx+2\int\limits_5^0f(x)\;dx
\]

Answer 2

You should be able to solve\[
\int\limits_5^0dx
\]Relatively simply.

Answer 3

Notice that: \[
\int \limits_5^0 f(x)\;dx = -\int \limits_0^5 f(x)\;dx = -\left(\int \limits_0^3 f(x)\;dx+\int \limits_3^5 f(x)\;dx\right)
\]

Answer 4

I got it. :) thanks for your help!