FRQ Volume Review

2010B, #1A Find the Area

x

y

y = 4 ln (3 – x)

Integral of Top - Bottom

1 pt for correct bounds1 pt for correct integral

1 pt for answerMUST be correct to 3 decimal places, 6.82 is wrong

2010B, #1B Revolve About y = 8

x

y

y = 4 ln (3 – x)

2 pts for correct integralAnything mathematically correct is acceptable

1 pt for answerMUST be correct to 3 decimal places

y = 8

R

r

2010B, #1C Base of an ObjectCross-Section | x-axis is a Square

x

y

y = 4 ln (3 – x)2 pts for correct integralin terms of x

1 pt for answerMUST be correct to 3 decimal places

2010A, #4A Find the AreaIntegral of Top - Bottom

x

y

y = 2√x

1 pt. Integral

1 pt. Anti-derivative

1 pt. Answer

2010A, #4B Rotated About y = 7

x

y

y = 2√xR

ry = 7

2 pt. Integral1 pt. bounds

2010A, #4C Base of ObjectCross-Section | y-axis is a Rectangle

x

y

y = 2√x

2 pt. integral1 pt. in terms of y

2008A, #1A Find the Area

x1y1

x2

y2

y1 = sin(πx)y2 = x3 – 4x

Integral of Top - Bottom

1 pt. Integral1 pt. Bounds1 pt. Answer

2008A, #1B Area Below y = –2

x1y1

x2

y2

y1 = sin(πx)y2 = x3 – 4x

Integral of Top - Bottom

1 pt. Integral

a = 0.5391889b = 1.6751309

Use Calculator to Find Intersections

1 pt. bounds

2008A, #1C Base of ObjectCross-Section | x-axis is a Square

x1y1

x2

y2

y1 = sin(πx)y2 = x3 – 4x

1 pt. integral1 pt. answer

2008A, #1D Base of ObjectCross-Section | x-axis, h = 3 – x

x1y1

x2

y2

y1 = sin(πx)y2 = x3 – 4x

1 pt. integral1 pt. answer

2009A, #4A Find the Area

x1

y1x2

y2

y1 = 2xy2 = x2

Integral of Top - Bottom1 pt. Integral

1 pt. Anti-derivative

1 pt. Answer

2009A, #4B Base of ObjectCross-Section | x-axis, A = sin (πx/2)

x1

y1x2

y2

y1 = 2xy2 = x2

1 pt. Integral

1 pt. antiderivative1 pt. ans

2009A, #4C Base of ObjectCross-Section | y-axis is a Square

x1

y1x2

y2

y1 = 2xy2 = x2

2 pt. integral1 pt. bounds