The area of a region in the plane

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Question from Rogerson, a student:

Please help me with this.

Find the area, S, of the shaded region enclosed by the given curve, the given line and the x-axis.

y = -x^2 + 1
line x = 2

thanks.

Rogerson,

I sketched the curve y = -x² + 1 and the line x = 2 and shaded the region in the plane bounded by these two curves and the x-axis.

region between the curves

The shade region is entirely below the x-axis and hence if you integrate -x² + 1 for x between 1 and 2 the value will be negative. The area of the shaded region is then minus this value.

Harley

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