Question

Evaluate the integral $\stackrel{1}{\underset{-1}{\int }}(3x-2)dx$.

Answer 1

${\int }_{-1}^1(3x-2)dx$

Let $f\left(x\right)=3x-2$

$f(-x)=3(-x)-2$

$f(-x)=-3x-2$

$f\left(x\right)$

${\int }_{-1}^1(3x-2)dx={\left|\frac{{3x}^2}{2}\right|}_{-1}^1-{\left|2x\right|}_{-1}^1=\frac{3}{2}(1-1)-2(1+1)$

$=\frac{3}{2}\left(0\right)-2\left(2\right)=-4$

${\int }_{-1}^1(3x-2)dx=-4$