Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an appropriate form so that a trigonometric substitution can be performed. 13 + 12x − x2

I don't see a square root sign anywhere, so I'll assume the integral is

First complete the square:

Now in the integral, substitute

so that

Under this change of variables, we have

so that

Under the right conditions, namely that cos(t) > 0, we can further reduce the integrand to

Expand the sine term as

Then

So the integral is

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.