Integration - Volumes Of Revolution Flashcards
(11 cards)
1
Q
How to integrate 4e^0.5x
A
8e^0.5x
2
Q
Equation for volumes of revolution
A
V = pi | y^2 dx
3
Q
If have like (e^0.5x -2) as y and square it, what’s the answer?
A
Need to expand it properly as has 2 terms…
e^x - 4e^0.5x + 4
4
Q
Where does volume formula give area of?
A
UNDER the graph
5
Q
If asked for area ABOVE graph… in vol. revolution q
A
- Find area under graph with formula
- Find volume of cylinder or wtv shape the whole thing wld make
- Subtract under graph from cylinder
6
Q
Volume of a cylinder
A
Pi r^2 x h
For graphs: piy^2 x (x2-x1)
7
Q
When using limits how to make life easier
A
Write EVERYTHING out (1 - 0 - 0) - (2/5 + 7pi) then simplify
8
Q
If graph has a straight line as part of it, how can u find the volume a simpler way?
A
Use volume of cone
9
Q
Volume of a cone
A
1/3pi h^2 b
10
Q
If given parametrics what order must u do everything?
A
- Change boundaries to t
- Dx/dt and substitute to cancel
- Y^2
11
Q
How to integrate (lnx)^2
A
Chain rule:
2lnx · 1/x
