How do you do this question?
1 answer:
Answer:
π/10
Step-by-step explanation:
When we rotate the region about the y-axis, we get something that looks like a volcano, or a bundt cake. Instead of slicing this into flat washers, we'll slice it in concentric rings, or "shells".
Each shell has a radius x, a thickness dx, and a height y. The volume of an individual shell is:
dV = 2π r h t
dV = 2π x y dx
Since y = x² − x³:
dV = 2π x (x² − x³) dx
dV = 2π (x³ − x⁴) dx
The total volume is the sum of all the shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π (x³ − x⁴) dx
V = 2π (¼ x⁴ − ⅕ x⁵) |₀¹
V = 2π (¼ − ⅕)
V = π/10
You might be interested in
Answer:
see below
Step-by-step explanation:
Put -1 where x is in each expression and evaluate it.
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You will find that the expression is zero when the numerator is zero. And you will find the numerator is zero when it has a factor that is equivalent to ...
(x +1)
Substituting x=-1 into this factor makes it be ...
(-1 +1) = 0
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Evaluating the first expression, we have ...
This first expression is one you want to "check."
You can see that the reason the expression is zero is that x+1 has a sum of zero. You can look for that same sum in the other expressions. (The tricky one is the one with the factor (x -(-1)). You know, of course, that -(-1) = +1.)
