Post #14

okay so this is totally late..ik ik..i thought i had did it..but it turns out i typed it in word on saturday november 21 and then forgot to put it in the blog because of craziness with my Georgia Vaction that was coming up and no one was ready for...
but..we learned about integration all week..
There were two types of integration. the first type was indefinite and the second was definite. you do the same thing for both except that for definite you see two numbers and at the end you have to plug them in and then subtract what you get by each other in order to get your answer. Remember that if it's indefinite then you have to put the plus 'c' but if it's definite then you just should have a number.

Then we learned about the change of variables which means that there is at least two differnet variables in the equation you are solving.
Then we learned about the area between the curves of graphs and the formula is bSa top equation minus the bottom equaion. in order to find a and b you need to set the equations equal to each other and then solve. what you solve for depends on what you're looking for or have in the equations. for instance if the area is on the y axis, then a and b need to be y values so the equations can be solved for x and opposite if the values need to be x values.
i kinda like the e integration the most. when you have the e integration, whatever it's raised to the e power will be your 'u' and 'du' will be the derivative of 'u'. here's an example:

e^4x-1dx
u=4x-1 du=4
now you rewrite the function as:
1/4{ e^u du, therefore
1/4e^4x-1+C is the final answer

Another type of integration that we learned is ln integration. so for this one just rmember that any time you have like [1/x] it'll be ln lxl plus c... these aren't too bad. An example of ln integration would be:

{1/5x-1dx
u= 5x-1 du=5dx
1/5 { 5/5x-1 dx
1/5 ln |5x-1| dx +C

I am not very good at change in variables substitution and area between curves substitution. I kinda understand e and ln substitution. I just do not know how to break things up in the other types of substitution and i have trouble knowing when to plug numbers in and finding where some of the numbers are coming from.
~Ellie~