Question

the graph of function h is shown below. let $g(x) = \int_{1}^{x} h(t) dt$.
evaluate $g(4)$.
$g(4) = \square$

Explanation:

Step1: Define g(4) via integral

$g(4) = \int_{1}^{4} h(t) dt$

Step2: Split area into shapes

Area = Triangle + Trapezoid

Step3: Calculate triangle area

Base = $4-3=1$, Height = $4-2=2$
Area of triangle: $\frac{1}{2} \times 1 \times 2 = 1$

Step4: Calculate trapezoid area

Bases = $2, 4$, Height = $3-1=2$
Area of trapezoid: $\frac{1}{2} \times (2+4) \times 2 = 6$

Step5: Sum the two areas

Total area = $6 + 1 = 7$

Answer:

7