10. (10 points) Evaluate the following definite integrals: 1. (3x +x 23 ) dix [. 4f (x) dx , given that [ f (x) dx = 23 and [ f (x) d = 8. 11. (10 points) A farmer wants to enclose a rectangular garden that borders a straight river. He needs no fence along the river. The area should be 3,500 square feet. The cost of the fence on one side (parallel to the river) is $10 per foot; the other two sides are to be constructed of less expensive fencing, at $7 per foot. What are the dimensions of the garden that will cost the least to fence in? Draw a diagram, label it appropriately with variables, express the quantity you want to minimize in terms of your variables, and solve for the optimal dimensions using calculus. Justify that the dimensions you find do yield the absolute minimum cost