Question

CalculusFind the volume by Revolutiony=x^2, x=0, y=4 in the first quadrant about the y-axis

Answer 1

`\begin{gathered} y=x^2 \\ x=0 \\ y=4 \\ 4=x^2 \\ √(4)=x \\ x=2 \\ V=\int A(x)dx \\ \\ A(x)=\pi r^2 \\ A(x)=\pi(x^2)^2=\pi x^4 \\ \\ V=\int_0^2\pi x^4dx=(\pi x^5)/(5)|^2_0=(\pi(2)^5)/(5)\text{ -0=}(32\pi)/(5) \\ The\text{ volume is }(32\pi)/(5) \end{gathered}`