How do you solve an integral problem?

Question

How to evaluate an integral which can be a definite integral or an indefinite inegral.

Answer 1

There are lots of "tricks" to solve an integral problem. For a definite integral, sometimes you can estimate the solution graphically by finding the approximate area under the curve of the function. Or, sometimes you can find a different function that approximates your function that you CAN integrate. Methods such as these pretty much make up a semester class. If you have a specific question, maybe we can help you solve it.

Answer 2

I'm going to assume you mean integrating a simple integral.

For a simple derivative we use the equation n*x^n-1. In this case we subtract one from the exponent and take the original number in the exponent (n) and multiple our base (in this case x) by n. For an integral we will do the opposite.

Lets integrate 3x². Our first step would be adding 1 to the exponent so in this case our exponent 2 would become 3. We would be left with 3x³ which would lead us to our second step of diving our base by the new value of the exponent. We would be left with (3/3)x³ which simplifies to x³. If the integral is indefinite we add +C to the end of the problem or we would evaluate using the bounds if it is definite.

This shows how to manually solve an integral but understanding the theory of solving an integral is just as important.