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Area, Volume, and Arc Length

Area, Volume, and Arc Length

Area, Volume, and Arc Length: Making Mercury: Free Fish Sticks True or False

1. Let R be the finite region bounded by the graphs y = x2, y = 6 – x, and x = 4. Which picture shows R as the shaded region? ->
2. Which of the following integrals give the area of the shaded region?

(I) 

(II) 

(III)  

(IV) -> (II) and (III)

3. Let R be the region bounded by the graphs of y = x and . Which of the following integrals give the area of R?

(I) 

(II) 

(III) 

(IV)  -> (I) and (III)

4. Let R be the region graphed below.

Which of the following integral expressions give the area of R?

(I)

(II) 

(III)   -> (III) only

5. Which of the following integrals gives the area of a right triangle whose non-hypotenuse sides have lengths 7 and 9? ->
6. Which of the following is the area of the unit circle? ->
7. A square has a diagonal of length 10. Which of the following expressions does NOT give the area of the square? ->
8. Below is a graph of the polar function r = f(θ).

What is the area of the shaded region? ->

9. What is the area of one petal of the graph of the polar function r = 1 + cos(3θ)? ->
10. What is the area of the shaded region?

->


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