Math 125 Test 4 6 points each April 13, 2005

Integrate

1. ∫ 4 dx

2. ∫ 3x dy

3. ∫ x²y dy

4. ∫ sec x tan x dx

5. ∫ sin²(4x²-2x + 8) + cos²(4x² - 2x + 8) dx

6. ∫3 sin x dx

7.

8.

9. ∫ csc² x dx

Evaluate the definite integral.

10.

11.

12. Find the differential dy for:

y = x² + tan x

13. Profits in the Airdale business obeys the formula P = -A³ + 15A² -48A - 6. How many should I raise?

14. A box with a square base is to have an open top. The area of the material in the box is to be 100 in². What should the dimensions be in order to make the volume as large as possible?

Find the area of the region bounded by

15. y = x² + x, y = 0, between x = 0 and x = 2

16. i. y = x³ - x² and y = 0 between x = 0 & x = 4