2413 A dog breeder has 40 feet of fencing to use for a rectangular dog run. If she puts the run next to the P-24+y garage, she only needs to use the wire for three sides. What dimensions will yield maximum area? 410 = 2+ x 12. Find the average value for the following functions on the given intervals. a. f(x)=3x [0,3] g(x)=2+3x f(x2)-F(x1) x2-x1 c. f(x)=x+1 [-2,1] 13. Use the Second Fundamental Theorem of Calculus to find F'(x). F(x)=sinx Cosx x=40-24 A=XY 4 = (40-2y) Y 7 = 401-2yz 0=4541 Y=10 X=20 15. Find the indefinite integrals: 2x a. 1-x dx = 1-x2 b. f (nx)dx V = lnx vzlhx ex c. ++ex sec dx v=4x8x d. sex dx = tanx tanx e. (2x+5)(x + 5x)'dx = xx f. fsin(2x) dx =2x e. v= x+5x du =2x+5dx sinx Jot dt b. sint dt .cos 1 I Cosx .- sin x 14. The graph below consists of line segments and a semicircle. Evaluate each definite integral. (x) (a) f(x) dx = (c) fmf (x) dx = (b) [1(x) dx = (0) 31(x) dx = Su du 08 + C 8