Question

Use the limit process to find the area of the region between f (x)=10x+8 and the x-axis on the interval [0,3]

Answer 1

Subdivide the area into n vertical rectangles, each of width
w=(3-0)/n.
The (x-)position of the ith rectangle is x(i)=(i-1)(3/n)=3(i-1)/n.
The height is
h(i)=10x(i)+8
The area is
a(i)=w*h(i)

The total area is therefore A

n
∑ a(i)
i=1

Evaluate the summation and calculate the area A by taking limit n → ∞.