Solution: A trough is filled with water and its vertical

Find the length of the curve.

Find the length of the curve.

Find the length of the curve (b) Find the area of the surface obtained by rotating the curve in part (a) about the -axis

(a) The curve , , is rotated about the -axis. Find the area of the resulting surface. (b) Find the area of the surface obtained by rotating the curve in part (a) about the -axis.

Use Simpsons Rule with to estimate the length of the sine curve ,

Use Simpsons Rule with to estimate the area of the surface obtained by rotating the sine curve in Exercise 5 about the -axis

Find the length of the curve

Find the area of the surface obtained by rotating the curve in Exercise 7 about the -axis.

A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom, 5 ft wide at the top, and 2 ft high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate.

A trough is filled with water and its vertical ends have the shape of the parabolic region in the figure. Find the hydro static force on one end of the trough.

Find the centroid of the region bounded by the given curve

Find the centroid of the region bounded by the given curve

Find the centroid of the region shown

Find the centroid of the region shown

Find the volume obtained when the circle of radius 1 with center is rotated about the -axis

Use the Theorem of Pappus and the fact that the volume of a sphere of radius is to find the centroid of the semi - circular region bounded by the curve and the -axis.

The demand function for a commodity is given by Find the consumer surplus when the sales level is 100

After a 6-mg injection of dye into a heart, the readings of dye concentration at two-second intervals are as shown in the table. Use Simpsons Rule to estimate the cardiac output

(a) Explain why the function is a probability density function. (b) Find . (c) Calculate the mean. Is the value what you would expect?

Lengths of human pregnancies are normally distributed with mean 268 days and standard deviation 15 days. What per cen tage of pregnancies last between 250 days and 280 days?

The length of time spent waiting in line at a certain bank is modeled by an exponential density function with mean 8 minutes. (a) What is the probability that a customer is served in the first 3 minutes? (b) What is the probability that a customer has to wait more than 10 minutes? (c) What is the median waiting time?