Expand the integral $\int_{0}^{\sqrt{a^2-x^2}}\left(x^2+y^2+a^2\right)dy$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int_{0}^{\sqrt{a^2-x^2}} x^2dy$ results in: $x^2\sqrt{a^2-x^2}$
The integral $\int_{0}^{\sqrt{a^2-x^2}} y^2dy$ results in: $\frac{\sqrt{\left(a^2-x^2\right)^{3}}}{3}$
The integral $\int_{0}^{\sqrt{a^2-x^2}} a^2dy$ results in: $a^2\sqrt{a^2-x^2}$
Gather the results of all integrals
Try other ways to solve this exercise
Get a preview of step-by-step solutions.
Earn solution credits, which you can redeem for complete step-by-step solutions.
Save your favorite problems.
Become premium to access unlimited solutions, download solutions, discounts and more!