(Homework) Make a sketch to show a case in which the area bounded by two curves

Note: Just guessed. No idea why.(Homework) Sketch the region and find its area.

1st part: Graph both functions. The bounded area is the part confined between the two. Thats where its shaded.2nd part: Follow the example instructions. Very clear.

(Example) Sketch the region and find its area.

(Homework) Sketch the region bounded by and and then

1st part: Use Wolfram to plot these functions. The calculator doesnt do absolute value.2nd part: Follow the example instructions.3rd part: You can answer the area part with the calculator with Area cant be negative. Just take the absolute value.

(Example) Sketch the region bounded by and and then

(Homework) Determine the area of the shaded region in the figure to the right by integrating with respect to y.

Note: Just follow the example instructions step-by-step. Pretty straight forward.

(Example) Determine the area of the shaded region in the figure to the right by integrating with respect to y.

(Homework) Express the area of the following shaded region in terms of

Part a: I guessed. Take the one with the 2 in front.Part b: To find the two limits take the given x functions, set them equal to each other and solve for y. and the answer is Then just subtract them from each other in the integral function.

(Homework) Find the area of the following region. Sketch

1st part: Just graph the two functions and pick the one that resembles it.2nd part: I just followed the example build.3rd part: Just plug-in the answer from part 2 and solve.

(Example) Find the area of the following region. Sketch

(Homework) Use the most efficient strategy for computing the area of the following region.

Note: Follow example. Simple.(Example) Use the most efficient strategy for computing the area of the following region.

(Homework) Find the area of the shaded region shown in the figure

Take the bottom function, set it equal to the top function, and solve for x. There are probably two values. Take the positive value as the limit you need. One is the limit you need. Put it into the dx integrals. NOT dy!For the first integral just subtract the bottom function and the top function. Now, put it in the first integral.For the second, subtract the bottom function from the middle function. It doesnt simplify, so just put it in and done.To solve the second part, just enter the answer to the first part into the calculator and solve.

(Homework) For the following region R, find the horizontal line

Note: I basically cheated. Whatever is the first digit after the equal sign, just plug that in where the x is. Seems to work every time.(Example) For the following region R, find the horizontal line

(Homework) A Lorenz curve

Part a: Same as example.Part b: Same as example.Part c: Be careful to watch for the wording exactly. When given a sequence of numbers, the lowest is most equitable, the highest is least equitable.Part d: Same as example.Part e: Use the formula . Just change the exponent to whatever Gini value youre given for each one. 1.2, 1.5, 2, 3, 4.Part f: Same as example.Part g: Same as example except for the last part. Integrate the Gini formula they give you like this

Just change the parentheses with whatever L(x) they give you.(Example) A Lorenz curve