Set Two
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Flying Heavy Metal Episode Two: Jet Set-Part 1 High Quality
Set Two
Can someone help me set up two integrals?
I need to find the volume of y = sqrt (x+1) , x=0, y=1, y=2; about x = -2 with two distinct integrals, which I believe we will use washer and cylindrical shells. Please help me set them up.
2 = √(x + 1) ....... find the intersection with y = 2
x = 3
1 = √(x + 1) ....... find the intersection with y = 1
x = 0
Shell method
V = 2π ∫ (x + 2) (2 - √(x + 1)) dx ..... from 0 to 3
let u² = x + 1 ; 2u du = dx
= 4π ∫ 2u - u² + 2u³ - u^4 du ... from 1 to 2
= 4π (u² - u^3/3 + u^4/2 - u^5/5) ... from 1 to 2
= 4π (4 - 8/3 + 8 - 32/5 - 1 + 1/3 - 1/2 + 1/5)
= 118π/15 units³
Disc method:
V = π ∫ (y² + 1)² - (2)² dy .... from 1 to 2
= π ∫ y^4 + 2y² - 3 dy
= π (y^5/5 + 2y³/3 - 3y) ... from 1 to 2
= π (32/5 + 16/3 - 6 - 1/5 - 2/3 + 3)
= 118π/15 units³
Answer: V = 118π/15 units³
Ready-Set-Grow Vol 2 Part 2 Of 7
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