The third blog of this detention I will start by explaining the area between curves. The formula is bSa top equation-bottom equation
1. draw the picture of the graphs
2. subtract the two equations from each other
3. put the like terms together and integrate the result
Next I will talk about trig inverse integration. The trig inverse integration formulas are: (sr=square root)
1. S du/sr(a^2-u^2)=-1/sr(u)arcsin u/a +C
2. S du/a^2+u^2=1/du(a)arctan u/a +C
3. S du/u sr(u^2-a^2)=1/du(a)arcsec lul/a +C
Another thing I will talk about is substitution. Substitution takes the position of derivative rules when integrating. The steps for substitution are:
1. Find a derivative of something else inside of the integral.
2. Set u equal to the non derivative found in the integral
3. Then take the derivative of u
4. Substitute back in
5. Solve
Example problem:
S (2x^2+5) (4x) dx u=2x^2+5 du=4x dx
S u du
1/4 u^2+C
1/4 (2x^2+5)^2+C
Also I am going to talk about taking implicit derivatives. The steps for taking implicit derivatives are:
1. Take the derivative of both sides like you would normally do
2. Everytime the derivative of y is taken it needs to be notated with either y ' or dy/dx
3. Solve for dy/dx or y ' as if you are solving for x.
For what I do not know is something like Find the area of the region enclosed by y=-4x^2+41x+94 and y=x-2 between x=1 and x=7.
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use the formula b(interation sign)a top - bottom.
ReplyDeleteyou find the top by plugging in both formulas to your calculator, or do it by hand.
a and b are 1 and 7... they give you that.
You do area as normal. You just use the formula but instead you do definite S top - bottom. You can easily find which border is the top by plugging in to your calculuator. The problems tells you that a and b are 1 and 7 so your definite integral is from 1 to 7. Integrate normally and plug in.
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