Find the area of the region bounded by the curves y = x^2 and y = cos(x). Give your answer correct to 2 decimal places.

Answer 1

Let c is intersection point of graphs of y = x² and y = cos(x). Area A what we have to find is equal:

A = ∫₀^c(cos(x) - x²)dx = (sin(x) - x³/3)₀^c.= sin(c) - c³/3.

Let use TI-84: C alc Menu, Intersaction command we get c =.82413231.

Because A = sin(.82413231) - .82413231³/3 ≈ 0.55

Answer: area A ≈ 0.55