Question

Find the area of the region bounded by the curves y = x2 − 1 and y = sin(x). Give your answer correct to 2 decimal places

Answer 1

To find the area of the region bounded by the curves y = x^2 - 1 and y = sin(x), we need to find the points of intersection between the two curves and set up an integral to calculate the area. Solve the equations to find the points of intersection, set up the integral, and evaluate it to get the area.

Step-by-step explanation:

The given question asks us to find the area of the region bounded by the curves y = x^2 - 1 and y = sin(x).

To find the area, we need to find the points of intersection between the two curves. Set the equations equal to each other and solve for x:

x^2 - 1 = sin(x)

We can't solve this equation algebraically, so we can use numerical methods or a graphing calculator to find the approximate values of x for which the curves intersect. Once we have the points of intersection, we can set up the integral to calculate the area between the curves in the given interval. Evaluate the integral and round the answer to 2 decimal places to get the final result.

Answer 2

The curves intersect at x = ±1.18. So, using symmetry, the area is

a = ∫[0,1.18] cos(x) - (x^2-1) dx