Evaluate the following definite integrals. () [( x+6 ) dx (in [(+1) dx (iv) (3x -7) dx ( v ) [ [-+ x-e2 + 2]dx If the marginal revenue for a commodity is R (x) =80-0.4x where x is the number of units sold, what is the total revenue function? If the marginal cost for a product is C (x) = 0.001x-0.1x +10, where x is the number of units produced and fixed cost of production is $3,500, what is the total cost function? LMN Ltd. manufactures pencils. The total cost of producing 50 pencils is $150. The marginal cost (in dollars) to manufacture x pencils is given as: C'(x) =2-0.01x (i) What is the fixed cost of the company? (ii) Find the total cost function of LMN Ltd. Sketch the graphs of y=x -6x +5 and y = 5 on the same axis, indicating the points of intersection. Hence, find the area of the region enclosed by the curve and the line. Sketch the graph of y = 2x and y = 4x on the same axes, indicating the points of intersection. Hence, find the area of the region enclosed by the curve and the line