By using the properties of definite integrals, the value of \(\int_{-5}^{5}\left(x+2\right)dx\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(20\)
\(I=\int\limits_{-5}^{5}\left(x+2\right)dx\)
$=\int\limits_{-5}^{0}(x+2)dx+\int\limits_{0}^{5}(x+2)dx$
$=\left[\frac{x^2}{2}+2x\right]_{-5}^{0}+\left[\frac{x^2}{2}+2x\right]_{0}^{5}$
$=\left[0-\frac{25}{2}+10\right]+\left[\frac{25}{2}+10\right]$
$=20$