Use the limit process to find the area of the region between f(x)= 10x + 6 and the x-axis on the interval [0,7].
A) $287$
B) $112$
C) $245$
D) $532$
E) $251$

Question

Use the limit process to find the area of the region between f(x)= 10x + 6 and the x-axis on the interval [0,7]. 
A) $287$
B) $112$
C) $245$
D) $532$
E) $251$

Quizplus · Accepted Answer

The area under the curve $f(x) = 10x + 6$ from $x = 0$ to $x = 7$ can be found using the definite integral of $f(x)$ over the interval $[0, 7]$. The definite integral of $f(x) = 10x + 6$ from $0$ to $7$ is calculated as follows:$$\int_{0}^{7} (10x + 6) dx = \left[5x^2 + 6x\right]_{0}^{7} = (5(7)^2 + 6(7)) - (5(0)^2 + 6(0)) = (245 + 42) - 0 = 287.$$Therefore, the area of the region between the curve and the x-axis over the given interval is 287 square units.

Use the Limit Process to Find the Area of the Region