Calculus/Calculus

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Expert: - 10/15/2008


Question
How would I definite integral that represents the area of the region enclosed by y = 4x – x2 and the x-axis.

Answer
I will assume the question is to be read as,
'How do I define the integral that represents the area of the region enclosed by y = 4x – x² and the x-axis.'

First, find the endpoints, and that's where the two curves cross.  One is the curve y = 4x - x² and the other is the x-axis, which is
y = 0.

Solving this will give you two values for x.

The answer is the integral (between these two values)(difference in the equations)dx.

The difference in the equations is (4x - x²) - 0 = 4x - x².

Find those two values and integrate away.

Calculus

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