6. Find the exact area of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area of the region. y = V1 - x2 and y = x2 + 2x + 1 7. The largest triangle with a base on the x-axis that fits inside the upper half of the unit circle y + x = 1 is given by y = 1 + x and y = 1 - x. See the following figure. What is the area inside the semicircle but outside the triangle? 1.54 0.5 -1.5 -1 -0.5 0 0.5 1.5 X -0.5- 8. Use shells to find the volumes of the given solids. Note that the rotated regions lie between the curve and the x-axis and are rotated around the y-axis. y = VI - x2, x =0, andx = 1 9, Use shells to find the volume generated by rotating the regions between the given curve and y = 0 around the x-axis. y= x =0, x =2, and the x-axis 10. Find the length of the functions over the given interval. y= - x + 25 from x = 1 to x = 4