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FRQ Volume Review

FRQ Volume Review. 2010B, #1A Find the Area. Integral of Top - Bottom. x. y = 4 ln (3 – x). 1 pt for correct bounds 1 pt for correct integral. y. 1 pt for answer MUST be correct to 3 decimal places, 6.82 is wrong. 2010B, #1B Revolve About y = 8. r. y = 8. x. R.

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FRQ Volume Review

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  1. FRQ Volume Review

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

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

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

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

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

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

  8. 2008A, #1A Find the Area Integral of Top - Bottom 1 pt. Integral 1 pt. Bounds 1 pt. Answer x1 y1 = sin(πx) y2 = x3 – 4x y1 y2 x2

  9. 2008A, #1B Area Below y = –2 Integral of Top - Bottom 1 pt. Integral Use Calculator to Find Intersections a = 0.5391889 b = 1.6751309 1 pt. bounds x1 y1 = sin(πx) y2 = x3 – 4x y1 y2 x2

  10. 2008A, #1C Base of ObjectCross-Section | x-axis is a Square 1 pt. integral 1 pt. answer x1 y1 = sin(πx) y2 = x3 – 4x y1 y2 x2

  11. 2008A, #1D Base of ObjectCross-Section | x-axis, h = 3 – x 1 pt. integral 1 pt. answer x1 y1 = sin(πx) y2 = x3 – 4x y1 y2 x2

  12. 2009A, #4A Find the Area Integral of Top - Bottom 1 pt. Integral 1 pt. Anti-derivative x1 y1 = 2x y2 = x2 x2 y1 y2 1 pt. Answer

  13. 2009A, #4B Base of ObjectCross-Section | x-axis, A = sin (πx/2) x1 1 pt. Integral y1 = 2x y2 = x2 x2 y1 1 pt. antiderivative y2 1 pt. ans

  14. 2009A, #4C Base of ObjectCross-Section | y-axis is a Square x1 2 pt. integral 1 pt. bounds y1 = 2x y2 = x2 x2 y1 y2

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