# Math Help - Evaluating definite integral without using antiderivatives?

1. ## Evaluating definite integral without using antiderivatives?

Hi there, this is my first post. I am having a difficult time parsing this question and I have not been able to find out where to start. If anyone has any insight I'd be very appreciative:

By the way, I looked at the example he counter-referenced, but I don't see the relation. Maybe I'm a mo-ron, but I don't see how the circle can be used to interpret this area. Any ideas?

Edit:

I forgot to mention that I've divided it into two integrals: one from o to the square root of five and the other from the square root of 5 to 5. I still don't know what to do from here without using antiderivatives.

2. Originally Posted by statelyplump
Hi there, this is my first post. I am having a difficult time parsing this question and I have not been able to find out where to start. If anyone has any insight I'd be very appreciative:

By the way, I looked at the example he counter-referenced, but I don't see the relation. Maybe I'm a mo-ron, but I don't see how the circle can be used to interpret this area. Any ideas?

Edit:

I forgot to mention that I've divided it into two integrals: one from o to the square root of five and the other from the square root of 5 to 5. I still don't know what to do from here without using antiderivatives.
$\int_0^5 2x \, dx - \int_0^5 \sqrt{25-x^2} \, dx$

sketch the graphs ...

first integral is the area of a triangle.

second integral is a quarter-circle.