\f50. Find the equation of the curve that passes through (2, 10) if its slope is given by dy = 6x + 1 dx69. Profit function. If the marginal profit for producing x units per day is given by P'(x) = 100 - 0.02x P(0) = 0 where P(x) is the profit in dollars, find the profit function P and the profit on 10 units of production per day.\fIn Problems 19-22, set up definite integrals that represent the shaded areas in the figure over the indicated intervals. 19. Interval [a, b] y = f(x) b y = g(r) Figure for 19-22 21. Interval [b, d]\f50. Consumers' and producers' surplus. Find the consumers' surplus and the producers' surplus at the equilibrium price level for each pair of price-demand and price-supply equa- tions. Include a graph that identifies the consumers' surplus and the producers' surplus. Round all values to the nearest integer. (A) p = D(x) = 70 - 0.2r: p = S(x) = 13 + 0.0012x2 (B) p = D(x) = 70 - 0.2r: p = S(x) = 130.006r\f47. Continuous income stream. The rate of flow (in dollars per year) of a continuous income stream for a 5-year period is given by f(t) = 2,500e0.05t Osis5 (A) Graph y = f(r) over [0, 5] and shade the area that rep- resents the total income received from the end of the first year to the end of the fourth year. (B) Find the total income received, to the nearest dollar, from the end of the first year to the end of the fourth year.