Graph the integrand and use areas to evaluate the integral.
-$$\int _ { 0 } ^ { 4 } 10 x d x$$
A) 160
B) 80
C) 8
D) 40

Question

Quizplus · Accepted Answer

The graph of the integrand is simply a straight line with slope 10 passing through the origin and (4,40). Therefore, the integral represents the area of a trapezoid with bases 0 and 4 and height 10. Using the formula for the area of a trapezoid, we get:
$$\frac{b_1+b_2}{2}h=\frac{0+40}{2}\cdot4=80$$
Therefore, the answer is B) 80.

Graph the Integrand and Use Areas to Evaluate the Integral ∫0410xdx\int _ { 0 } ^ { 4 } 10 x d x∫04​10xdx

Graph the Integrand and Use Areas to Evaluate the Integral $\int _ { 0 } ^ { 4 } 10 x d x$