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Math Help - Evaluating definite integral without using antiderivatives?

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    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.
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    Quote Originally Posted by statelyplump View Post
    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.
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