Question

use the properties of the definite integral to find $int_{b}^{a}\frac{sqrt{5}}{2}g(x)dx$, if possible, given that $int_{a}^{b}g(x)dx=-3$. write the exact answer. do not round. if it is not possible, write np for your answer.

Explanation:

Step1: Use integral property

$\int_{b}^{a}g(x)dx=-\int_{a}^{b}g(x)dx$. So $\int_{b}^{a}g(x)dx = 3$.

Step2: Factor out constant

$\int_{b}^{a}\frac{\sqrt{5}}{2}g(x)dx=\frac{\sqrt{5}}{2}\int_{b}^{a}g(x)dx$.

Step3: Substitute value

$\frac{\sqrt{5}}{2}\times3=\frac{3\sqrt{5}}{2}$.

Answer:

$\frac{3\sqrt{5}}{2}$