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If f(x)=8x +2 find the exact area under the curve from x=0 to x=2.

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You do not need Calculus for this question, since this results in a trapezoid.
The two parallel sides have lengths of 2 and 18 and the distance between them is 2

Area = 2(2+18)/2 = 20

if you insist on Calculus

Area = [integral](8x+2)dx from 0 to 2
= |4x^2 + 2x| from 0 to 2
= 16 + 4 - 0 = 20
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