1. FRQ Volume Review

2. 2010B, #1A Find the Area x y y = 4 ln (3 – x) Integral of Top - Bottom 1 pt for correct bounds 1 pt for correct integral 1 pt for answer MUST be correct to 3 decimal places, 6.82 is wrong

3. 2010B, #1B Revolve About y = 8 x y y = 4 ln (3 – x) 2 pts for correct integral Anything mathematically correct is acceptable 1 pt for answer MUST be correct to 3 decimal places y = 8 R r

4. 2010B, #1C Base of an Object Cross-Section | x-axis is a Square x y y = 4 ln (3 – x) 2 pts for correct integral in terms of x 1 pt for answer MUST be correct to 3 decimal places

5. 2010A, #4A Find the Area Integral of Top - Bottom x y y = 2√x 1 pt. Integral 1 pt. Anti-derivative 1 pt. Answer

6. 2010A, #4B Rotated About y = 7 x y y = 2√x R r y = 7 2 pt. Integral 1 pt. bounds

7. 2010A, #4C Base of Object Cross-Section | y-axis is a Rectangle x y y = 2√x 2 pt. integral 1 pt. in terms of y

8. 2008A, #1A Find the Area x1x1 y1y1 x2x2 y2y2 y 1 = sin(πx) y 2 = x 3 – 4x Integral of Top - Bottom 1 pt. Integral 1 pt. Bounds 1 pt. Answer

9. 2008A, #1B Area Below y = –2 x1x1 y1y1 x2x2 y2y2 y 1 = sin(πx) y 2 = x 3 – 4x Integral of Top - Bottom 1 pt. Integral a = 0.5391889 b = 1.6751309 Use Calculator to Find Intersections 1 pt. bounds

10. 2008A, #1C Base of Object Cross-Section | x-axis is a Square x1x1 y1y1 x2x2 y2y2 y 1 = sin(πx) y 2 = x 3 – 4x 1 pt. integral 1 pt. answer

11. 2008A, #1D Base of Object Cross-Section | x-axis, h = 3 – x x1x1 y1y1 x2x2 y2y2 y 1 = sin(πx) y 2 = x 3 – 4x 1 pt. integral 1 pt. answer

12. 2009A, #4A Find the Area x1x1 y1y1 x2x2 y2y2 y 1 = 2x y 2 = x 2 Integral of Top - Bottom 1 pt. Integral 1 pt. Anti-derivative 1 pt. Answer

13. 2009A, #4B Base of Object Cross-Section | x-axis, A = sin (πx/2) x1x1 y1y1 x2x2 y2y2 y 1 = 2x y 2 = x 2 1 pt. Integral 1 pt. antiderivative 1 pt. ans

14. 2009A, #4C Base of Object Cross-Section | y-axis is a Square x1x1 y1y1 x2x2 y2y2 y 1 = 2x y 2 = x 2 2 pt. integral 1 pt. bounds