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231 Unit I Beginnings Flashcards | StudBud

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Computing the area under a curve

One may multiply in and out of integrals things like

231 Unit I Beginnings

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Preliminary understanding of the integral

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1
One may multiply in and out of integrals things like
numbers
trig functions
negative signs
variables only if squared
2
Computing the area under a curve
involves rotation around an axis
always requires integration
uses dx to represent the width of rectangles
can sometimes be done with geometry
3
I did how many hours of calculus work this week?
more than 5
2-5
1-2
none
4
Derivatives and integrals
yield the same answer for a constant function
always use the power rule or reverse power rule
use the limit in their foundational definitions
are operations that can undo each other
5
Which would you pick for "u" in ∫sin²∅ cos∅ d∅
sin∅d∅
cos∅
d∅
sin∅
6
U sub is derived from
the Pythagorean Thm
the product rule
the Principia
the chain rule
7
If a function is rotated around the x axis
it may require squaring the denominator
it may have, as the height of the "cylinder," dx
it may have, as the height of the "cylinder," dy
it may require trig sub after rooting
8
The cylindrical shell method requires
a different formula than disks
cylinders
shells
knowledge of arc length
9
The washer method is used when
TWO functions are rotated around and axis
you need functions cleaned
a function is rotated around the x axis
a function's rotation removes volume from another's rotation
10
If one observes the integral of du/u, one AUTOMATICALLY thinks
tabular integration
logarithmic integration
washer method
integration by parts