Calculus 2

Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.

$y = x^2 + 2$

$y = 0$, $x = 0$, $x = 2$

Use the shell method to determine the volume formed by the bounded region rotated about the x-axis.

$y = x^2$, $y = 0$, $x = 2$

Determine the volume of the solid generated by rotating the function about the x-axis on $[0,3]$

$y = \sqrt{9 - x^2}$

Evaluate $\int x \, sin(x) \, dx$

$\displaystyle \int sin^3x \, cos^4x ,\ dx$

Evaluate $\int x^4 \, ln \, 3x \, dx$

$\displaystyle \int cos^3x \, dx$

Determine the volume of the solid generated by rotating the function about the y-axis on $[0,4]$

$y = \sqrt{x}$

Evaluate $\displaystyle \int \frac{5x}{e^{2x}} \, dx$

$\displaystyle \int sin^2x\, dx$