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. (5 points)

Answer 1

the intersection must be found numerically, looking at the graph.....

They are (-0.637,-0. 595) and (1.4096, 0.987) with the sine curve on top of the parabola

integral [ sin x - x^2 - 1] = -cos x - (1/3)x^3 - x

plugging in the limits as x--> -0.637 and x--> 1.4096

result in and respectively

The subtracting them the result is , which makes sense

because most of the slab of the region is below the x-axis