# MFE2-hw8 - Math for Econ II Written Assignment 8(28 points...

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Math for Econ II, Written Assignment 8 (28 points)Due Friday, April 11thNew York UniversityPlease write neat solutions for the problems below. Show all your work. If you only write the answer with no work,you will not be given any credit.Write your name and recitation section number.Staple your homework if you have multiple pages!1. (3 pts) Supposefis even,R-1-2f(x)dx= 3, andR42f(x)dx= 5. Either findR41f(x)dx, or show there is notenough information to findR41f(x)dx.2. Evaluate the following integrals:(a) (2 pts)Z211 +x3x2dx(b) (2 pts)Z10(x2+ 2)2dx(c) (2 pts)Z1-1(x7-x5+x3-x)dx3. (2 pts) Explain what is wrong with the following calculation of the area under the curve1x2fromx=-1 tox= 1:Z1-11x2dx=h-1xi1-1=-1 + 1 = 0.4. (3 pts) Suppose the area under the curveexfromx= 0 tox=ais four times the area under the curve 2e2xfromx= 0 tox=b. Solve forain terms ofb. (in other words, writea=(some formula involvingb))5. (3 pts) You have a bank account, whereB(t) is your balancetyears after you open the account. Initially, your