Substitution takes the place of the derivative rules for problems such as product rule and quotient rule.
The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
e integration:whatever is raised to the e power will be your u and du will be the derivative of u.
For example:e^2x-1dxu=2x-1 du=2
rewrite the function as:1/2{ e^u du, therefore
1/2e^2x-1+C will be the final answer.
limits:Rules for Limits:…
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
3. if top degree is less than bottom degree, the answer is 0
Im still having problems with integration but i do understand the e one since we went over that that one class
Subscribe to:
Post Comments (Atom)
say we need to integrate x^2 + 2x^4 + 8x^3
ReplyDeletethe steps include adding one to the exponent, then dividing that number by the coefficiant..
so, lets solve the problem:
1/3x^3 + 2/5x^5 + 8/4x^4
simplify...
1/3x^3 + 2/5x^5 + 2x^4
integrating is simple like this...i always switch it around and take the derivative of the answer choices and not integrate if it's too difficult...like the substitution problems..
Remember for ln integration, the top has to be the derivative of the bottom, if that is so, your integral would be ln | whats on the bottom|+C. For other integrals, lets say you need to integrate 2x+5. You would add an x and times the front by the reciprocal. So the answer would be x^2+5x. Hope this helps!
ReplyDeleteif you have trouble with integration and have time, just take the derivative of the answer choices and see if one of them is the integral given. just reminding you you can do that :)
ReplyDeleteOk, with integration, just remember it's doing what you can to undo a derivative. It's the opposite of a derivative. You also need to remember that in integration, there are no chain rules, product rules, or quotient rules, so you will need to use substitution to force the integral to work. For substitution, you'll have two parts: a derivative and an "origional function." You will use the "origional function" for u and it's derivative as du. Ln integration is also easy. It's when the the derivative of the bottom is the top, making u the bottom. the integral is then ln |u| (and + c depending on if it's infinite or finite).
ReplyDeleteokay, integrating is basically the opposite of taking the derivative of something. all you have to do is raise the exponent of the x value by 1, then you take the reciprocal of the new exponent and multiply the number in front of the x value by it.
ReplyDeleteExample: 2x^2
first you gotta raise the exponent: 2x^3
then you take the reciprocal and multiply: 2/3x^3 and you're done!