SOLUTION: If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the interval [0,pie] a) find the area of rigion R b)Define R as the region bounded above by the g

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Question 1189664: If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the interval [0,pie]
a) find the area of rigion R
b)Define R as the region bounded above by the graph of the function f(x)=root x and below by the graph of the function g(x)=1 over the interval[1,4].find the volume of the solid of the revolution generated by revolving R around the Y-axis.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
No pie in math problems (unless it's a pie chart).
Use the Greek letter pi.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
If R is a region between the graphs of the function f(x)=sinx and g(x)=cosx over the interval [0,pie]
a) find the area of rigion R
~~~~~~~~~~~~~~~


            In this post,  I will solve problem  (a),  ONLY. 


If you plot the graphs of the functions f(x) = sin(x) and g(x) = cos(x) over the interval [0,pi],

you will see that  g(x) >= f(x)  at 0 <= x <=   and  g(x) <= f(x)  at  <= x <= .

Also, you can get it algebraically.



In any case, the area of the region R is the sum of two integrals


    area(R) =  + .



First integral equals

    (sin(x) + cos(x))  from 0 to ,  which is   - 1 = .



Second integral equals

    (-cos(x) - sin(x))  from  to ,  which is  1 +  = .


After adding the integral values, we get

    area(R) =  +  =  = 2.828427  (rounded).    ANSWER

Part (a) is solved.



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