Math

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]

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  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 → ∞.

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