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# Area under a curve

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1. I have inserted a picture of 2 different ways I have worked the area of a curve out for Y=4e^2x

Would someone be able to tell me if one of them is right please?
2. (Original post by ak1992)

I have inserted a picture of 2 different ways I have worked the area of a curve out for Y=4e^2x

Would someone be able to tell me if one of them is right please?
Neither is correct. Use the result that
3. Try to use a bit of care in your notation. You answer shows a very common misconception when dealing with integration of composite functions. In this case we have where

The case where is just of the form is particularly easy to deal with as the differential of is just
and needs to divide the result of integrating in a way that treats as if it were just .

Hence , and
4. (Original post by ak1992)
I thought that was only for Intergration?
And how precisely do you find the area under a curve? By integration.

The area under a curve between the point and of a function is given by .

In your case, the area under the curve of between and is given by
5. I think it's important for you to go back and understand the content before continuing with any more questions. Otherwise you're just blindly trying to apply algorithms that you don't understand.

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