Question

Find the area of the region bounded by the graphs of the following equations.y=5x+6,y=0,x=3andx=8.

Answer 1

Given the equations

y=5x+6,

y=0,

x=3and

x=8

we can build the region

the area is given by the defined integral

$\int _3^8\:5x+6$$\frac{5x^2}{2}+6x|^8_{3^}$$\frac{5(8)^2}{2}+6(8)-\frac{5(3)^2}{2}-6(3)$$167.5$

Area= 167.5 units^2