Expert: Sherman D. - 9/22/2005

Question
Hi, thanks for you help with an earlier question.  I got there in the end.  I have 2 more questions that I'm stumbling over and would appreciate your guidance.  Here goes;

Q1.  What is the area of the region which is bounded by the positive x-axis and by the graph of the function  y=(1-x)(x-5)  all divided by x

Q2.  What is the solution to the following initial value problem

    dy/dx = -2(ysin((1/2)x)^2  (x>0, y>0),  y=2/pi when x=1/2pi


Thanks for you invaluable help.

Richard

Answer
Q1.) I hope this is what you are wanting.

y = ((1 - x)(x - 5))/x
1 <= x <= 5

for a graph, so that you can figure it out, go to www.calculator.com/calcs/GCalc.html

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Q2.) Since i have never worked with dy/dx, here is what i can deduce from your problem

-2(ysin((1/2)x)^2)

-2((2/pi)sin((1/2)(pi/2)))^2

-2((2/pi)sin(pi/4))^2

-2((2/pi) * .707106781)^2

-2(1.414213562/pi)^2

-2(2/(pi^2))

-4/(pi^2)

Sorry i couldn't be of much more help.

Its just that you are giving me calculus or precalculus problems that i hadn't done.