Graph the integrand and use areas to evaluate the integral.
-$$\int _ { 1 } ^ { 3 } 10 x d x$$
A) 80
B) 4
C) 40
D) 20

Question

Quizplus · Accepted Answer

The graph of $y=10x$ is a straight line with a slope of 10 passing through the point $(0,0)$. The integral represents the area under this line between $x=1$ and $x=3$.

To find the area, we can visualize a rectangle with base $2$ (the distance between $x=1$ and $x=3$) and height $10$, which corresponds to the integrand. The area of this rectangle is $20	imes 2 = 40$. Therefore,

$$\int _ { 1 } ^ { 3 } 10 x d x = 40$$

and the correct answer is $\boxed{	ext{(C)}}$.

Graph the Integrand and Use Areas to Evaluate the Integral ∫1310xdx\int _ { 1 } ^ { 3 } 10 x d x∫13​10xdx

Graph the Integrand and Use Areas to Evaluate the Integral $\int _ { 1 } ^ { 3 } 10 x d x$