File Edit View History Bookmarks Iools Help Sample Commands Assignment 1 Take a

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File Edit View History Bookmarks Iools Help Sample Commands Assignment 1 Take a screen shot sil e openvellum.ecollege.com/#178 ( a , 5 ] . ii. Find the area of the function over the interval [ 1 , 5 Math 262-04 Fall 2015 TTH 2:30 PM Chase Assignment 1 MyMathLab Page: - + Automatic Zoom 3 Main Menu Mathematica 2. For each of the following functions, input the function into Mathematica. Then produce the requested outputs Sample Commands Assignment 1 Assignment 2 (a) f(x)-x2 - 2x + 2 i. Plot the graph on the interval [1,5 ii. Find the area of the function over the interval [1, 5] (b) g(x) e* i. Plot the graph on the interval [-4,2] Find the area of the function over the interval [-4,2 3. Calculate the following sums: 600 (a) (0.05k) 1000 (b) > (0.05k + 0.001k2) k=1 5:07 PM 9/28/2015

Explanation / Answer

2)

a) area=integral[1 to 5] x^2 -2x +2 dx

integral x^n =(x^(n+1))/(n+1)

[1 to 5] (x^3)/3 -2(x^2)/2 +2x +c

[1 to 5] (x^3)/3 -(x^2) +2x +c

[ (5^3)/3 -(5^2) +2*5 +c]-[ (1^3)/3 -(1^2) +2 +c]

=(125/3 -25 +10+c)-(1/3 -1 +2)

=125/3 -25 +10+c -1/3 +1 -2 -c

=124/3 -16

=76/3

=25.33

b)e^(5x)

area =integral[-4 to 2] e^(5x) dx    integral e^(ax) =(e^(ax) )/a +c

=[-4 to 2] (e^(5x))/5 +c

= (e^(5*2))/5 +c - (e^(5*(-4)))/5 -c

=(e^10)/5 - (e^-20)/5

=[1/5][e^10- e^-20]

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