Problem #1: Evaluate the following integral. f(4x+ 1)8 dx Enter your answer as a symbolic Problem #1: function of x, as in these Do not include '+ C' in your answer. examples Problem #2: Evaluate the following integral. J'xs A +10 4 Enter your answer as a symbolic Problem #2: function of x, as in these Do not include '+ C ' in your answer. examples Problem #3: Evaluate the following integral. 2 f i@y & Enter your answer as a symbolic Problem #3: function of x, as in these Do not include '+ C ' in your answer. examples Problem #4: Find the particular solution of the following differential equation satisfying the indicated condition. r _ 2. | = y'=21y% y = ;7 whenx=0. Enter your answer as a symbolic Problem #4: function of x, as in these Do not include 'y ="' in your answer. examples Problem #5: Find the general solution to the following differential equation. dy = 3y dx 4 (A) y = e(3/4)* + C (B) y = Ce(3/4)x (C) y = e(4/3)x +C (D) y= 3/4 + C (E) y = Ce(4/3)x (F) y= Cx3/4 (G) y= x4/3 + C (H) y = Cx4/3 Problem #5: Select +Problem #6: Find the general solution to the following first order linear differential equation. xy y' = 2+ 10 (A) y = Ce-1/[1(x + 10)] (B) y = e-1/[1(x2+ 10)] + c (C) y = C(x2 + 10)1/2 (D) y = e-1/[2(x2+ 10)] + C (E) y = Ce-1/12(x- + 10)] (F) y = (x2 + 10)1/1 + C (G) y = (x2 + 10) 1/2 + C (H) y = C(x2 + 10) 1/1 Problem #6: SelectProblem #7: A 40 gallon tank is filled with pure water. Water which has a concentration of 6g of salt per gallon flows into the tank at a rate of 4 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 4 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()/40, where S(z) is the total amount of salt in the tank at time #, in grams. '(7), the rate of change of salt in the tank over time, is equal to the [rate in] [rate out]. dS _ 5y S0 dS _ 5y _ S0 s _3_50 as _3_50 as (A)E'% 10 (B)dr_24 40 (C)dr_2 (D)dz'z (E)dt = -0 40 10 =6 40 dS _ g _SO) (G dS_ 3 _SO g dS_ 3 _S0 () dr_6 10 (G) d 20 10 (H) dt ~ 20 40 Problem #7: Childsmath do = J: w Examples of How = to Enter Symbolic Answers Symbolic functions must be entered using notation similar to the examples given below. e Do NOT include the name of the function or an equal sign. (i.e., do NOT include anything like 'f =' in your answer.) e Decimal numbers cannot be a part of any symbolic function. Integer numbers (positive, negative, and 0) and fractions are allowed. e Below are some examples. Example Function of x V5 e *+2In(mx/3) sqrt(5-exp(-x)+2*1n(pi*x/3)) iy hello can someone please help me with these calculus question alongside how to input it on the software "childsmath" as well please example will be on the end! with image. question #5,6,7 are multiple choice