EXAMPLE 4 Evaluate the following integrals by interpreting each in terms of area

Question

EXAMPLE 4 Evaluate the following integrals by interpreting each in terms of areas.

SOLUTION (a) Since

we can interpret this integral as the area under the curve

we get

(b) The graph of

3 9 ? x2 dx 0 Evaluate the following integrals by interpreting each in terms of areas. we can interpret this integral as the area under the curve we get x2 + y2 = 9, which shows that the graph of f is a quarter-circle with radius in the top figure. Therefore, The graph of y = x ? 1 is the line with slope shown in the bottom figure. We compute the integral as the difference of the areas of the two triangles:

Explanation / Answer

I'm not exactly sure which parts you need answering so i'll solve the integrals of both

area of a circle is pi*r^2, therefore for part a the area is (1/4)*pi*r^2

area=9pi/4

for part b you are given two triangles, area=(1/2)*b*h

area of the top triangle is:(1/2)*3*2=3

area of the bottom triangle is:(1/2)*1*1=1/2 or 0.5

a1-a2(negative area)=2.5

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