Calculus Blog - Makeup

So the last week was amazing...I completely forgot about school, and it felt great :-)

Looks like in the process, I completely forgot about doing my blog as well :-)

Anyway, so I guess what I can explain is... e^x integration

For example:

integral of e^2x is just (1/2)e^2x+C

The derivative of e^x is just e^x times derivative of x.

So the integral is the opposite of its derivative times e^x. Kind of hard to explain...it just works....

Like for example...The integral of

(2x+4)e^(x^2+4x) is just e^(x^2+4x) + c because the derivative of u was already there. You only have to put the opposite whenever its not there...like the problem before.

Had it been 2e^2x then the integral would just be e^2x + c. You can check your answer by taking the derivative of that...which it works out.

The other thing I understand pretty well is ln integration...

1/x is ln|x|

So 2/x is 2ln|x|+C and 2/(1-x) is 2ln|1-x|+c

So anyway, ln integration is easy...

What else is there...

Today we learned how to finally do those ones with d/dx in front of the integral symbol...it turned out really easy actually...
You just cancel the integration and the d/dx and you plug in the top x or x^2 or whatever it is. So that's easy.

Overall the integration packet was not that bad...just really long. The rram, lram, mram, and trapezoidal ram took the longest because of crazy fractions and stuff though.

Anyway, that wraps up my post.

-John