Find the area between −𝑥2 and −𝑥 from 𝑥 = −1 to 𝑥 = 1. (Hint: Drawing a picture may help. These functions intersect at 𝑥 = 0 and 𝑥 = 1.)

1. Find the area between −𝑥2 and −𝑥 from 𝑥 = −1 to 𝑥 = 1. (Hint: Drawing a picture may help. These functions intersect at 𝑥 = 0 and 𝑥 = 1.)

2. Consider the region bounded by the functions 𝒚 = 𝟔𝒙 and 𝒚 = −𝒙𝟐 + 𝟕, where the functions intersect at the points (𝟏, 𝟔) and (𝟐, 𝟑), and where 𝑦 = −𝑥2 + 7 is the top and right-most function in the bounded region, which means that 𝑦 = 𝑥6 is the bottom and left-most function in

the bounded region. Calculate the volume of the solid generated by revolving the region about the line 𝒚 = 𝟕 using the Washer (Disk) Method: