Question

If
int_{1}^{4}f(x)dx =-2 and int_{2}^{4}f(x)dx =4
then find int_{2}^{1}f(x)dx... think I got it but not quite :)

Answer 1

I'm sure you know that \(\int_1^2 f(x)dx+\int_2^4 f(x)dx=\int_1^4 f(x)dx\), which implies \(\int_1^2 f(x)dx=-2-4=-6 \implies \int_2^1 f(x)dx=6.\)