A seven-year-old child wants to turn a patch of the backyard into a sandbox . You, the child's babysitter, must comply , or else nobody will be happy. The plot is in the shape of a right triangle with side lengths equal to 5 ft, 12 ft, and 13 ft. Suppose the child wants the density of sand in the sandbox to be p(x) g/ft^2 , where x is the distance away from the 12-ft side. (The child is very specific about their wants)a) Write a Riemann sum that approximates the total amount of sand in this sandbox. Start by slicing into n slices; make sure to explain clearly how you are slicing and all the details of your work, including what your notation means, b) Write a definite integral that gives the exact amount of sand in this sandbox.

1. A seven-year-old child wants to turn a patch of the backyard into a sandbox. You, the child's babysitter, must comply, or else nobody will be happy. The plot is in the shape of a right triangle with side lengths equal to 5 ft, 12 ft, and 13 ft. Suppose the child wants the density of sand in the sandbox to be p(x) g/ft2, where r is the distance away from the 12-ft side. (The child is very specific about their wants.) (a) (5 points) Write a Riemann sum that approximate the total amount of sand in this sandbox. Start by slicing into n slices; make sure to explain clearly how you are slicing and all the details of your work, including what your notation means. (b) (2 points) Write a definite integral that gives the exact amount of sand in this sandbox. A 12 13 5