Integral Calculus

Locate the centroid of the plane area bounded by the equation \(y^2=4x\), \(x=1\) and the x-axis on the first quadrant.

Find the length of arc of the parabola \(x^2=4y\) from \(x=-2\) to \(x=2\).

Find the surface area (in square units) generated by rotating the parabola arc \(y=x^2\) about the x-axis from \(x=0\) to \(x=1\).

The area enclosed by the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is revolved about the line \(x=3\). What is the volume generated?

The area in the second quadrant of the circle \(x^2+y^2=36\) is revolved about the line \(y+10=0\). What is the volume generated?

The area bounded by the curve \(y^2=12x\) and the line \(x=3\) is revolved about the line \(x=3\). What is the volume generated?

Given the area in the first quadrant bounded by \(x^2=8y\), the line \(y-2=0\) and the y-axis. What is the volume generated when the area is revolved about the line \(y-2=0\)?

Find the volume (in cubic units) generated by rotating a circle \(x^2+y^2+6x+4y+12=0\) about the y-axis.

Given the area in the first quadrant by \(x^2=8y\), the line \(x=4\) and the x-axis. What is the volume generated by revolving this area about the y-axis.

Find the moment of inertia, with respect to x-axis of the area bounded by the parabola \(y^2=4x\) and the line \(x=1\).