1) First find f\' and then find f. f \'\'(x)=x^3 -2x +1 f \'(1)= 0 f(1)=4 2) Fin
ID: 2828484 • Letter: 1
Question
1) First find f' and then find f.
f ''(x)=x^3 -2x +1
f '(1)= 0
f(1)=4
2) Find a formula for Rn and compute the area under the graph as a limit.
f(x)=x^2 +7x , [6,11]
3) Calculate the Riemann sum R(P,f,C) for the given function, partition, and choice of sample points. Also, sketch the graph of f and the rectangles corresponding to R(f,P,C).
f(x)=2x+3
P=[-4,-1,1,4,8]
C=[-3,0,2,5]
4) Write the integral as a sum of integrals without absolute values and evaluate:
the integral is going from 0 to 5. I just couldn't figure out how to put it on there.
Explanation / Answer
1.f''(x)= x^3 - 2x + 1
f'(x)= integration of f''(x) = x^4/4 - x^2 + x
f (x)= integration of f'(x) = x^5/20 -x^3/6 + x^2/2
What is RN?
Let y=f(x)?0 for x?[a,b].
Then the area of the region between the graph of the function and the x-axis
over the specified interval is:
Area=lim[n-->inf] [(b-a)/n]?[i=1 to n] f[a+i(b-a)/n]
a=6, b=11
Area=lim[n-->inf] [(11-6)/n]?[i=1 to n] f[6+i(11-6)/n]
4. integration of mode of x2 -4x + 3
when mode open with +ve sign
integral will be x3/3 - 4x2/2 +3x
when mode will open with -ve sign
integral will be -(x3/3 -4x2/2 + 3x)
When limit is 0 to 5.
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