If someone could explain how to do this problem (in detail please) or show me how, I would greatly appreciate it.

1-2. The function [tex]f(x)\, =\, \sqrt{\strut R^2\, -\, x^2\,}[/tex] has domain [tex]\left[-R,\, R\right].[/tex] Assume [tex]0\, \leq\, a\, \leq\, R.[/tex] We wish to evaluate the following integral:

. . . . .[tex]\displaystyle \int_0^a\, \sqrt{\strut R^2\, -\, x^2\,}\, dx[/tex]

(This corresponds to the shaded area in the graphic.)

Tragically, we do not know how to find an antiderivative for [tex]f(x).[/tex] We will learn this later in the course. Instead, evaluate the integralgeometricallyby splitting the shaded area into the area of a triangle (which is pretty easy) plus the area of a circular sector (which will entail an inverse trig function).

I tried to figure it out in some scribbles on the side.

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