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anonymous

  • 5 years ago

There;s a property that says that if f(x) is greater than or equal to 0, on an interval [a,b] then the definite integral of f(x) from a to b, is also greater than or equal to zero. Is the opposite of this property true? The opposite being:"If f(x) is less than or equal o zero then the definite integral is also less than or equal to zero."

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  1. anonymous
    • 5 years ago
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    Yes, here's an example: f(x)=-x^2 from a=1 to b=2 integrate: -x^3/3 from 1 to 2 =-7/3 The reason is that you are calculating area below the curve.

  2. anonymous
    • 5 years ago
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    Where did you get the 3? So the integral is negative, but the area is positive?

  3. anonymous
    • 5 years ago
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    Yes, that is because you read it from left to right. It may be easier to explain the process by going backwards: when you integrate, you anti-differentiate. So take the derivative: Drop the ^3 down and subtract 1 from the exponent. Then the 3/3 cancels to 1 and we get -x^2. If the integral were from 2 to 1 (rather than 1 to 2) it would be positive.

  4. anonymous
    • 5 years ago
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    Oh I see, got it. Thanks!

  5. anonymous
    • 5 years ago
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    Np :)

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