Integration by Substitution - Area of a Circle (2011)

The equation of a circle centred at (0,0) and with radius r is y=(r^2-x^2)^0.5. By integrating y w.r.t. x from x=0 to x=r, we get the area of quarter of a circle with radius r. At 3:20 the substitution x=rsinθ is used where θ is the angle between r and the vertical side of the triangle. We could also use the substitution x=rcosθ where θ is the angle between r and the x-axis.