Evaluate the following integral. S Jox (9x + 1)8 dx Problem #2: Evaluate the following integral. Sixters + x4 et + 18 dx Problem #3: Evaluate the following integral. Lx(In(4x Problem #3: x(ln(4x))5 dx Problem #4: Find the particular solution of the following differential equation satisfying the indicated condition. y' = 21 y; y = when x = 0. 14 Problem #4: Enter your answer as a symbolic function of x, as in these examples Do not include 'y = 'in your answer. Problem #5: Find the general solution to the following differential equation. Problem #5: Problem #6: Problem #7: dy dx Select C (A) y=x6/5 + C (B) y=e(5/6)x+C_(C) y = Ce(5/6)x (D) y = e(6/5)x + C (E) (F) y = Cx6/5 (G) y=x5/6+ C (H) y = Ce(6/5)x Just Save Problem #5 Your Answer: Your Mark: Select (F) || Problem #6: Find the general solution to the following first order linear differential equation. (A) 6y 5x (A) y = C(x + 7)/3 (B) y (E) y = (x + 7)/3 + C (F) y = Just Save Problem #6 Your Answer: Your Mark: dS dt dS dt || || (x+7) = Select C Attempt #1 Attempt #2 Attempt #3 Problem #7: A 77 gallon tank is filled with pure water. Water which has a concentration of 5g of salt per gallon flows into the tank at a rate of 7 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 7 gallons/min. Find a differential equation describing the rate of change of salt in the tank. Hint: The concentration of salt in the tank is S(t)/77, where S(t) is the total amount of salt in the tank at time t, in grams. S'(t), the rate of change of salt in the tank over time, is equal to the [rate in] - [rate out]. Submit Problem #5 for Grading 35 5 S(t) 77 77 Just Save S(t) 77 Attempt #1 Attempt #2 Attempt #3 Submit Problem #6 for Grading (B) (G) (x + 7)/2 +C (C) y = dS dt dS dt || e1/[2(x + C(x + 7)/2 (G) y = Ce1/[2(x +7)] 5 5 S(t) 11 (C) (H) dt ds dt || Submit Problem #7 for Grading || 5 S(t) 77 11 5- S(t) 77 +7)] + C (D) y (H) y (D) y = Cx5/6 || 5 S(t) 77 = e1/[3(x + 7)] + C Ce-1/[3(x. +7)] (E) = 45 dt 35 S(t) 11