Calculus 2

The first-quadrant area is bounded by the curve $y^2 = 4x$, the x axis, and the line x = 4 is rotated about the y axis. Find the volume generated: (a) By the ring method (b) By the shell method

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.

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

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

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

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

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

Given $x^3 = y^5 + 2$, find the arc length from $y = 1$ to $y = 3$ and the surface area when the arc is rotated about the x-axis.

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

$y = \sqrt{x}$

$\displaystyle \int cos^4(5x)\, dx$

$\displaystyle \int \frac{tan^3x}{sec^2x} \, dx$

Evaluate $\displaystyle \int \frac{x \, sin^{-1}x}{\sqrt{1-x^2}} \, dx$

Evaluate$\displaystyle \int e^{cos^{-1}x}\, dx$

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

$\displaystyle \int tan^3x \, sec^3x \, dx$

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

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

Find the area enclosed by $x^2 + y^2 = r^2$.

Evaluate $\int x^2 \, cos(x) \, dx$

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

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

Evaluate $\displaystyle \int \frac{sin(\frac{1}{x})}{x^3} \, dx$