Bounded by curves

Question

Find the area of the region bounded by the curves y = x^2 - 1 and y = cos(x). Give your answer correct to 2 decimal places

Answer 1

First, find the x values where the curves are equal.  This will give us our bounds.  Then you take the sum of the integrals of both functions.

 

x² - 1 = cos(x)

 

 

You can use a graphing calculator to graphically find the two points of intersections.   Make sure your calculator is in radians mode.  Take the x values in which they intersect.

 

x₁ = a

x₂ = b

 

 

Then, once you find your x values the two curves have in common, take the sum of the definite integrals.

 

^b_a ∫(x² - 1)dx + ^b_a ∫cos(x)dx