Use graphical evidence and known area facts to find:[br] a. [math]\int^2_0\left(2x+1\right)dx[/math] b. [math]\int^1_0\sqrt{1-x^2}dx[/math]
a. [math]\int^2_0\left(2x+1\right)dx[/math][br] = shaded area[br] =[math]\left(\frac{1+5}{2}\right)\times2[/math][br] =3.[br]b. [math]\int^1_0\sqrt{1-x^2}dx[/math][br] = shaded area[br] =[math]\frac{1}{4}\left(\pi r^2\right)[/math]where r=1[br] =[math]\frac{\pi}{4}[/math].