Chapter 6 - Section 6.2 - Volume - 6.2 Exercises - Page 447: 34

a) $3.54459$ b) $2.66521$

$y=x^2$ $y=\sqrt{1-x^2}$ a) Intersection points: $\sqrt{1-x^2}=x^2; 1-x^2=x^4$ $x_1=-0.786151;x_2=0.786151$ $\pi\int_{-0.786151}^{0.786151}((1-x^2)-x^4)dx=3.54459$ b)Intersection points: $\sqrt{1-x^2}=x^2; 1-x^2=x^4$ $y_1=0;y_2=0.618034$ $y_3=0.618034;y_4=1$ $\pi\Big(\int_{0}^{0.618034}(1-y^2)dy+\int_{0.618034}^{1}(y)dy\Big)=2.66521$