Answer:
1) ∫₀¹ 2π x (x − x²) dx
4) ∫₀¹ π ((√y)² − y²) dy
Step-by-step explanation:
The solid formed is a hollow, upside down cone. We can either use washer method or shell method to find the volume.
If we use washer method, the thickness of the washers is dy. The outside radius is R = x₂ = √y, and the inside radius is r = x₁ = y.
Therefore, the volume of each washer is:
dV = π (R² − r²) t
dV = π ((√y)² − y²) dy
The total volume is the sum of all washers from y=0 to y=1.
V = ∫ dV
V = ∫₀¹ π ((√y)² − y²) dy
If we use shell method, the thickness of each shell is dx. The radius of each shell is r = x. The height of each shell is h = y₂ − y₁ = x − x².
Therefore, the volume of each shell is:
dV = 2π r h t
dV = 2π x (x − x²) dx
The total volume is the sum of all shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π x (x − x²) dx
Answer:
Step-by-step explanation:
For a known standard deviation a confidence level of 99% we may consider Z=<span>2.576.
So, the confidence interval would be calculated by:
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Considering the given data, with a 99% cofidence, it can be said that the true mean of hours of study in a typical week for first-year college students is between 14.282 and 16.318.