Calculating a Definite Integral

Hello, I'm a freshman in highschool trying to get a headstart into calculus, so please excuse my limited knowledge in the subject.

Anyways, I have this integral

I have some sort of idea on how to solve it. Something about taking the anti-derivative.

The answer is 3, but I would like to know how to get there step by step, I'm having a hard time comprehending my calculus book.

Re: Calculating a Definite Integral

If is an antiderivative of , then the area under the curve between x = a and x = b is given by . In other words, evaluate an antiderivative of your function, evaluate it at x = b and x = a, and then evaluate the difference between these values.

Re: Calculating a Definite Integral

How would I find the antiderivative of though?

Unfortunately, I've only learned the Power Rule and its counter part. Even then it was just one term.

Thanks for your reply.

Re: Calculating a Definite Integral

The antiderivative of a sum/difference is equal to the sum/difference of antiderivatives. So you can work out the antiderivative of each term.

It would help if you rewrote your function as .

Re: Calculating a Definite Integral

Ahh, I see it now. Would the antiderivative of the aforementioned function be ? I know I could just check if the difference of is 3 to check, but I just want to make sure I'm doing this right.

Re: Calculating a Definite Integral

Quote:

Originally Posted by

**ReneG** Ahh, I see it now. Would the antiderivative of the aforementioned function be

? I know I could just check if the difference of

is 3 to check, but I just want to make sure I'm doing this right.

That is correct.