In a chemical reaction a certain compound changes into

Question

1. Find the indefinite integral.

a. ∫9/(5 - 4x) dx

b. ∫(x² - 2x)/(x³ - 3x²)dx

c. ∫(x³ - 6x - 20)/(x + ) dx

2. Find the definite integral.

a. ₀∫³ 1/√(1+x)dx

b. ₀∫^√2 1/√(4-x²)dx

c. ₂∫³(2x-3)/√(4x-x²) dx

3. Use the Disk Method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = √x, y = 0, and y = 3 about the line x = 3.

4. Use the Shell Method to find the volume of the solid generated by revolving the plane region y = √x, y = 0, and x = 4 about the line x = 6.

5. In a chemical reaction, a certain compound changes into another compound at a rate proportional to the unchanged amount. There is 40 grams of the original compound initially and 35 grams alter 1 hour. When will 75 percent of the compound be changed?

6. Find the arc length of the graph of the function y = 2x^3/2 + 3 over the closed interval [0, 9].