AP Calculus BC - Solids of Revolution - Vertical

Primary Input (Functions, Interval, Revolution Axis)

Expression 17: "f" left parenthesis, "x" , right parenthesis equals negative StartFraction, "x" squared Over 5 , EndFraction positive 11 halves

Expression 18: "g" left parenthesis, "x" , right parenthesis equals 1 half

Expression 19: left bracket, "x" Subscript, 1 , Baseline less than or equal to "x" less than or equal to "x" Subscript, 2 , Baseline , right bracket Cannot use an inequality here.

Expression 20: "x" Subscript, 1 , Baseline equals 1.5

negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline

"R" Subscript, "a" "d" "i" "u" "s" , Baseline

Expression 21: "x" Subscript, 2 , Baseline equals 4.5

negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline

"R" Subscript, "a" "d" "i" "u" "s" , Baseline

Revolve about line X.

Expression 23: "X" equals 0

negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline

"R" Subscript, "a" "d" "i" "u" "s" , Baseline

Expression 24: "R" Subscript, "e" "v" "o" "l" "u" "t" "i" "o" "n" , Baseline equals 1

Secondary Input (Cross Section)

Expression 26: "E" Subscript, "n" "a" "b" "l" "e" , Baseline equals 0

Expression 27: "x" Subscript, "s" "h" "e" "l" "l" , Baseline equals 1.8

"x" Subscript, 1 , Baseline

"x" Subscript, 2 , Baseline

Perspective View

Expression 29: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals 1

negative pi

Expression 30: theta Subscript, "v" "e" "r" "t" "i" "c" "a" "l" , Baseline equals negative 0.4 5

negative pi

Expression 31: theta Subscript, "c" "i" "r" "c" "u" "l" "a" "r" , Baseline equals 0

negative pi

Visual Representation Construction

"x"

"y"

Perspective

"x" Subscript, 1 , Baseline equals 1.5

"x" Subscript, 2 , Baseline equals 4.5

"x" equals 0

Statistics

"V" "o" "l" "u" "m" "e" equals Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, 2 pi StartAbsoluteValue, "x" minus 0 , EndAbsoluteValue left parenthesis, StartAbsoluteValue, "f" left parenthesis, "x" , right parenthesis negative "g" left parenthesis, "x" , right parenthesis , EndAbsoluteValue , right parenthesis "d" "x" equals 155.5

"S" "u" "r" "f" "a" "c" "e" "A" "r" "e" "a" equals Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, 2 pi StartAbsoluteValue, "x" negative 0 , EndAbsoluteValue StartRoot, "f" prime left parenthesis, "x" , right parenthesis squared positive 1 , EndRoot "d" "x" positive Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, 2 pi StartAbsoluteValue, "x" minus 0 , EndAbsoluteValue StartRoot, "g" prime left parenthesis, "x" , right parenthesis squared positive 1 , EndRoot "d" "x" equals 150.1