Page 231 - Calculus Demystified

218 CHAPTER 8 Applications of the Integral
y = f (x)

a b

Fig. 8.1

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Fig. 8.2

Fig. 8.3

If we can express the area of the slice at position x as a function A(x) of x,
then (see Fig. 8.4) the volume of a slice of thickness x at position x will be about
A(x) · x.If P ={x 0 ,x 1 ,...,x k } is a partition of the interval [a, b] then the
volume of the original solid object will be about
V = A(x j ) · x.

j

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