Question

Integration of (x+2) dx from a to b.​

Answer 1

Explanation:

$\\{\mathtt \red{\int_{a}^{b}( x+2) d x}}$

Apply the Sum Rule: $\mathtt\pink{\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x}$

$\\ \mathtt \blue{=\int_{a}^{b} x d x+\int_{a}^{b} 2 d x}$

$\boxed{\mathtt \green{=\frac{b^{2}-a^{2}}{2}+2 b-2 a}}$