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Topic review (newest first)
V = ∫2πx(f(x)-g(x))dx
That's just integration by recognition. We know that if you differentiated , you'd get .
So, if we want the answer to be half of that, we need to half the thing we're differentiating.
Using this backwards shows that .
No problem. This is all fairly new to me, but hopefully someone can
ohh, ok. thanks. i feel like a retard now. hehe
For each microscopic y position, imagine a thin disc
I am integrating along the y-axis, not the x-axis.
Click on graph to make bigger.
but what happens with the y = 1? i need it to find the limits. it can't be the upper limit because the graphs don't intersect there. they intersect when x = e in this equation: y = ln x, so the upper limit should be e. correct me if i am wrong and please tell me why i am wrong.
y = ln x
Draw a graph and note are going to integrate from
y = 0 to y = 1.
because of pi r^2 for area. (disk method, might be called)
From an integral table:
Great answer, but I wish I knew how to
do the integral without the table lookup.