Chapter 5.5, Problem 317E

The area of the top half of an ellipse with a major axis that is the x-axis from $x=-1$ to a and with a minor axis that is the y-axis from $y=-b$ to b can be written as ${\displaystyle {\int }_{-a}^{a}b\sqrt{1-\frac{x^2}{a^2}dx}}$ .Use the substitution $x=a\cos t$ to express this area in terms of an integral of a trigonometric function. You do not need to compute the integral.