22Find the particular solution that satisfies the differenti

22)Find the particular solution that satisfies the differential equation f \'(x)=(1/3)x-5 and initial condition and 21)Use the Midpoint Rule n = 4 to approximate the area of the following region f(y)=1/4y, [1,4]

22) Well first we need to find the integral of the equation f(x)=x^2/6-5x+C you never gave us the initial condition but to find the equation you are looking for you would just input the x and f(x) value given ex: say f(0)=2 2=0-5(0)+C C=2 f(x)=x^2/6-5x+2 Note this may not be the correct case as I do not have the initial condition you can message me and I will get back to you but you do not have the full question. 21)4-1=3 3/4 is the interval for the 4 triangles they are [1,7/4], [7/4,10/4], [10/4,13/4], [13/4,4] now we find the four midpoints: 11/8, 17/8, 23/8, and 29/8. Now we find the four areas by using height times width or (f(11/8)+f(17/8)+f(23/8)+f(29/8))*3/4=30/16=15/8

$22)Find the particular solution that satisfies the differential equation f \'(x)=(1/3)x-5 and initial condition and 21)Use the Midpoint Rule n = 4 to approximat$

22Find the particular solution that satisfies the differenti

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