I have 2 triangle faces. i have 3 rectanglar faces. i have 6 vertices. i have 9 edges. what am i?
1 answer:
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Answer:
The volume for the solid of revolution is and its value is 401.43623.
Step-by-step explanation:
Since the function is rotating over the y-axis and it is a function in terms of x we can use Shell integration which general formula is given by
a) Setting up the integral.
We are given one end point for x which is x = 2, but we are not given the other, so we can set y = 0 on the given equation to get:
Notice that the exponential function is not going to be equal to 0, so we get the other endpoint for the interval as
which give us
Thus we integate from x = 0 to 2, so we will get:
And we can simplify that to
b) Using a calculator to evaluate the integral.
We can use a calculator to write the integral including the interval to get:
And its value rounded to 5 decimal places is