Evaluate the following integral: `int_0^asqrt(a^2-x^2)dx`

Explanation

Given, `int_0^asqrt(a^2-x^2)dx`

Let x=asiny


dx=acosydy

=`int_0^(pi/2)sqrt(a^2-a^2sin^2y)acosydy`

=`int_0^(pi/2)(a^2cos^2y)dy`

=`int_0^(pi/2)(a^2cos^2(pi/2-y))dy`

=`int_0^(pi/2)(a^2sin^2y)dy`

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