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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.