17th post

alright, we just reviewed this week, so i am going to go over integration. Integration is pretty much the opposite of a derivative.

there are two types of integration, definite integration and indefinite integration.

indefinite integration is easy, you just take the equation, and do this to it, lets say the equation is x^3+2x^2

to take the integral of something, first you have to raise the exponent by one, so lets take the first part of the problem, x^3, and do that to it. it becomes x^4. Now, you just multiple the whole thing by the inverse of the new exponent. so it would become (1/4)x^4.

then you do the same thing to the second part of the problem. 2x^2 becomes 2x^3, then you have to multiply, and it becomes (2/3)x^3

then you put the two parts back together like normal, and it becomes (1/4)x^4+(2/3)x^3.

but we are not done yet!! for indefinite integrals, you always have to add C at the end of the equation, so your final answer becomes: (1/4)x^4+(2/3)x^3+C

and for definite integrals, you just do the same thing, but for definite integrals, they give you a point, and you just plug in the x value from the point, and you do not add the C at the end!!! so lets just use the example problem from indefinite integration, but they'll also give you a point, let's say (2,2) for example. You would integrate it normally, and get (1/4)x^4+(2/3)x^3, then you plug in your x value, which is 2. so then you get (1/4)(2)^4+(2/3)(2)^3, and after that you can just put it into your calculator, which I do not have with me, and you'll just get some number as your answer. So for definite integration, you'll get a a number answer, and for indefinite integration, you'll get an equation.