91Ó°ÊÓ

Explain what is wrong with the statement. The function \(P(x)=x^{2} e^{x}\) is a cumulative distribution function.

Find the center of mass of a cone of height \(5 \mathrm{cm}\) and base diameter \(10 \mathrm{cm}\) with constant density \(\delta \mathrm{gm} / \mathrm{cm}^{3}\).

Set up definite integral(s) to find the volume obtained when the region between \(y=x^{2}\) and \(y=5 x\) is rotated about the given axis. Do not evaluate the integral(s). $The\quad x -axis$$

give an example of: A distribution with a mean of \(1 / 2\) and median \(1 / 2\)

Construct and evaluate definite integral \((s)\) representing the area of the region described, using: (a) Vertical slices (b) Horizontal slices Enclosed by \(y=x^{2}\) and \(y=6-x\) and the \(x\) -axis.

(a) In polar coordinates, write equations for the line \(x=1\) and the circle of radius 2 centered at the origin. (b) Write an integral in polar coordinates representing the area of the region to the right of \(x=1\) and inside the circle. (c) Evaluate the integral.

Construct and evaluate definite integral \((s)\) representing the area of the region described, using: (a) Vertical slices (b) Horizontal slices Enclosed by \(y=2 x\) and \(x=5\) and \(y=6\) and the \(x\) -axis.

Explain what is wrong with the statement. The function \(P(t)=e^{-t^{2}}\) is a cumulative distribution function.

Show that the area formula for polar coordinates gives the expected answer for the area of the circle \(r=a\) for \(0 \leq \theta \leq 2 \pi\)

Set up definite integral(s) to find the volume obtained when the region between \(y=x^{2}\) and \(y=5 x\) is rotated about the given axis. Do not evaluate the integral(s). $$The\quad y -axis$$