Integral Calculus 02

The area bounded by the curve $$y=x^2$$ , the x-axis and the line $$x=1$$ is rotated about the x-axis. Determine the volume generated?

Find the volume of the solid generated when the area bounded by the curve $$y=\sqrt[]{x}$$ , the y-axis, and the line $$y=2$$ is rotated about the y-axis.

The area common to parabolas $$y^2=x$$ and $$x^2=y$$ is revolved about the 𝑦 – axis. Find the volume generated.

Find the volume of the solid form by rotating the area bounded by the curves $$y=x^2+1$$ , the 𝑥 – axis from $$x=0$$ to $$x=2$$ about the line $$x=-2$$ .

Find the surface area generated by revolving a rectangle of side 4 cm x 3 cm about the 4 cm side.

Find the centroid of a semi-circular arc of radius 𝑟.

Determine the volume generated by rotating an equilateral triangle of side measuring 10 cm each.

Find the volume generated by rotating a circle $$x^2+y^2+6x+4y+12=0$$ about the y-axis.

Find the coordinates of the centroid of the area bounded by the curve $$y=x^3$$ , the line $$x=2$$ and the x-axis.

Find the moment of inertia with respect to 𝑦 – axis of the area bounded by the parabola $$y^2=8x$$ and $$x=2$$ in the first quadrant.