frq volume review
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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. - PowerPoint PPT PresentationTRANSCRIPT
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