Browse Questions

# Evaluate the definite integral$\int\limits_{-1}^1(x+1)dx$

Toolbox:
• $\int\limits_a^b f(x)dx= F(b)-F(a)$
• $\int x^ndx=\Large\frac{x^{n+1}}{n+1}+c$
Given $I=\int \limits_{-1}^1 (x+1)dx$

On itntegrating we get,

$I=[\large\frac{x^2}{2}+x]$

Applying the limits we get

$\bigg(\Large\frac{1^2}{2}+1 \bigg)-\bigg(\frac{(-1)^2}{2}+(-1)\bigg)$

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

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