Explain why fluid pressure on a surface is calculated using horizontal representative rectangles instead of vertical representative rectangles.

How will you spend your average life expectancy of 78 years? The bar graph shows the average number of years you will devote to each of your most time-consuming activities. Exercises 21-22 are based on the data displayed by the graph. According to the U.S. Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend on each of these activities?

The fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet). Assume that the engine is approximately 3 feet above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic foot. Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine.

The region bounded by the graphs of y = 2√x, y=0, x=3, and x=8 is revolved about the x-axis. Find the surface area of the solid generated.

Fnd the volume of the solid generated by revolving the region bounded by the graphs of the equations about the $x$-axis.

$$y=\frac{1}{\sqrt{3 x+5}}, \quad y=0, \quad x=0, \quad x=2$$

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval. f(x) = x² + 4x, [0, 4]

Use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given line.

$y=3 x-x^2, \quad y=x^2, \quad$ about the line $x=2$

g(x) = 4 / (2-x), y=4, x=0

Which of the following requires more work? Explain your reasoning. (a) A 60-pound box of books is lifted 3 feet. (b) A 60-pound box of books is held 3 feet in the air for 2 minutes.

(a) usea graphing utility to graph the region bounded by the graphs of the equations, (b) find the area of the region analytically, and (c) use the integration capabilities of the graphing utility to verify your results. f(x)=x^4-4x², g(x)=x²-4

Use the integration capabilities of a graphing utility to approximate the arc length.

$$y=\frac{1}{x+1}, \quad[0,1]$$

Write a definite integral that represents the arc length of the curve over the indicated interval and observe that the integral cannot be evaluated with the techniques studied so far

$$y=\frac{1}{x+1}, \quad[0,1]$$

A barn is 100 feet long and 40 feet wide. A cross section of the roof is the inverted catenary $y=31-10\left(e^{x / 20}+e^{-x / 20}\right)$. Find the number of square feet of roofing on the barn.

Find the area of the following surfaces using a parametric description of the surface. The half-cylinder $\{ ( r , \theta , z ) : r = 4,0 \leq \theta \leq \pi , 0 \leq z \leq 7 \}$