calc quiz 3

find area between two equations

1. set equations equal to each other

2. solve for x (limits)

3. pick number between limits and test in both equations

   1. whichever is higher is top

4. set up integral (bounds as b and a) (actual: top-bottom)

5. integrate and solve

Area split (if the top equation is diff on different intervals)

1. set equations equal to each other

2. solve for x (limits)

3. pick number between limits and test in both equations

4. add up multiple integrals with diff top-bottom with respective bounds

5. integrate individually and add up

when to use disk/washer or shell

when you are slicing perpendicular to axis = DISK WASHER

when you are slicing parallel to acis = SHELL

x axis: y=

y axis: x =

If your function is y = f(x):

• Rotating around x-axis → Washer

• Rotating around y-axis → Shel

volume (disk)

1. given 1 equation

2. set r = to equation (whole thing: y=)

3. V = pi(integral (bounds)(equation)²dx

4. integrate

volume (washer)

1. given two equations

2. test number between bounds to find bigger (outer)

3. V = pi(integral(bounds)(outer-inner)²dx

4. integrate

Volume (shell)

1. given 1 equation

2. r = equation

3. V = 2pi(integral(bounds)Radius(height)dx

4. integrate

Inverse func on graph

no two x values have the same y value

• horizontal line test

monotone funcs

strictly increasing or strictly decreasing

ex. a<b and f(a)<f(b)

inverse func points

every (x,y) becomes (y,x)

domain and range switch

IFT

f^-1)’(b)= 1/f’(a) = (1/f’(f^-1(b))

IFT problem

trig derivatives

• sinx

• cosx

• tanx

• cotx

• ssecx

• cossecx

• cosx

• -sinx

• sec²x

• -cossec²x

• sec(x)tan(x)

• -cossec(x)cot(x)