### Home > APCALC > Chapter 4 > Lesson 4.2.2 > Problem4-56

4-56.

Ji Hee is trying to evalute the integrals in the parts (a) through (c) below. She already knows that $\int _ { 0 } ^ { x } g ( m ) d m = \frac { 4 x + 1 } { x + 2 }$. Help her calculate:

1. $2 \int _ { 0 } ^ { 3 } g ( m ) d m$

Solve for the area by substituting every $x$-value in the given equation with $3$. Simplify.

$2\int_{0}^{3}g(m)dm=2\left ( \frac{4(3)+1}{3+2} \right )=2\left ( \frac{13}{5} \right )=\frac{26}{5}$

2. $\int _ { - 1 } ^ { 0 } g ( m ) d m$

See part (a).

3. $\int _ { - 1 } ^ { 5 } g ( m ) d m$

See parts (a) and (b).