I am doing some practice problems for my exam tomorrow and I am having a bit of trouble when it comes to certain steps.
I need to find the area of surface of revolution. I need to just write down the expression whatever that means.
1. Find the area of the surface generated by revolving the curve y = x^3, 0 < x < 2, about the axis.
Here goes:
a = 0, b = 1, y = x^3, dy/dx = 3x^2
Sqrt 1 + (3x^2)^2
= 1 + 3x^2
This is where I became very confused.
2) If a force of 90 N stretches a spring 1m beyond its natural length, how much work does it take to stretch the spring 5m beyond its natural length?
I don't know what F(x) is.
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Edited by stapel -- Reason for edit: Attempting to display multi-line formatting.
I need to find the area of surface of revolution. I need to just write down the expression whatever that means.
1. Find the area of the surface generated by revolving the curve y = x^3, 0 < x < 2, about the axis.
Here goes:
a = 0, b = 1, y = x^3, dy/dx = 3x^2
Sqrt 1 + (3x^2)^2
= 1 + 3x^2
Code:
S= {1 2TT (x^3) (1+3x^2)dx = 2TT ?
}0
2) If a force of 90 N stretches a spring 1m beyond its natural length, how much work does it take to stretch the spring 5m beyond its natural length?
I don't know what F(x) is.
Code:
W= {5 90xdx= ?x^2dx |5 90/4?
}1 |1
Edited by stapel -- Reason for edit: Attempting to display multi-line formatting.