Question

Evaluate the integral:
${\int }_{-1}^1(x+1).dx$

Answer 1

${\int }_{-1}^1(x+1).dx$

Let

$F\left(x\right)=\int (x+1).dx$

$F\left(x\right)=\frac{x^2}{2}+x$

Now,

${\int }_{-1}^1(x+1).dx$

$=F\left(1\right)-F(-1)$

$=(\frac{(1{)}^2}{2}+1)-(\frac{(-1{)}^2}{2}+(-1\left)\right)$

$=(\frac{1}{2}+1)-(\frac{1}{2}-1)$

$=\frac{3}{2}=\frac{1}{2}$

$=2$