\f(1 point) Consider the area shown below. The top curve (in blue) is y = va, and the bottom curve (in red) is y = , and we have used the notation Dy for Ay. (Click on the figure for a larger version.) Write a Riemann sum for the area, using the strip shown: Riemann sum = > Now write an integral that gives this area where a = and b Finally, calculate the exact area of the region, using your integral area =[1 point) Consider the volume of the region shown below, which shows a hemisphere of radius 5 mm and a slice of the hemisphere with width Dy 2 by. Write a Riemann sum for the volume, using the sliee shown: Riemann sum 2 E Now write an integral that gives this volume 5. . . ... fa _ ::: where a = 555 and b = Finally, calculate the exact volume of the region, using your integral volume = = [include yhjts) (1 point) Each of the following integrals represents the area of either a triangle or part of a circle, and the variable of integration measures a distance. In each case, say which shape is represented, and give the radius of the circle or base and height of the triangle. You will find it useful to make a sketch of the region, showing the slice used to find the integral, labeling the variable and differential on your sketch. Then evaluate the integral to find the area. A. So 5x dx Which is the shape of the region being integrated? OA. Triangle OB. Part of a circle radius, or base and height = (If you are entering a base and height, enter them separated by a comma, e.g., 4, 3) area = B. fyl V11 - h2 dh Which is the shape of the region being integrated? OA. Triangle OB. Part of a circle radius, or base and height = (If you are entering a base and height, enter them separated by a comma, e.g., 4, 3) area =(1 point) Consider the area shown below. The curve drawn is * + y- = 37, and we have used the notation Dy for Ay. (Click on the figure for a larger version.) Write a Riemann sum for the area, using the strip shown: Riemann sum = > sqrt(37-y*2) Dy Now write an integral that gives this area sqrt(37-y*2)dy where a = 0 and b sqrt37 Finally, calculate the exact area of the region, using your integral area =(1 point) Consider the volume of the region shown below, which shows a right circular cone with top radius 3 cm and height 10 cm. We have used the notation Dy for Ay. Dy Write a Riemann sum for the volume, using the strip shown and the variable y: Riemann sum = > Now write the integral that gives this volume: volume = where a = and b Finally, calculate the exact volume of the region, using your integral. volume = (include units)