Question

How would we approach this problem?

If \[\int\limits_{2}^{4}5f(x)+2 dx=3 \] then \[\int\limits_{2}^{4}f(x)dx=\]...

Answer 1

Use the properties of definite integrals ( http://www.sosmath.com/calculus/integ/integ02/integ02.html), and then use algebra to solve for the integral in question.

First step:
\[
\int_{2}^{4} (5f(x) + 2) \ dx = \int_{2}^{4} 5f(x) \ dx + \int_{2}^{4} 2 \ dx = 3
\]

Try seeing if you can do the rest.

Answer 2

did you find the answer @hpfan101 ?

Answer 3

Yes I did! And thank you @andrewyates!