Page 234 - Calculus Demystified
P. 234
Applications of the Integral
CHAPTER 8
Fig. 8.7 221
√3
2
b b b
b
Fig. 8.8
triangular slice at position x has area
√
3
2 √ 2
A(x) = · 2 1 − x 2 = 3(1 − x ).
4
Finally, we may conclude that the volume we seek is
1
V = A(x) dx
−1
1 √
2
= 3(1 − x )dx
−1
1
√ x 3
= 3 x −
3 −1
√ 1 −1
= 3 1 − − (−1) −
3 3
√
4 3
= .
3
