SOLUTION: please help Find the area bounded between a) f(x) = 1/x and g(x) = x^2 on the interval [1,3] b) f(x) = x^3 - 3x^2 + 2x and x-axis on the interval [1,2] c) f(x) = si

Algebra ->  Finance -> SOLUTION: please help Find the area bounded between a) f(x) = 1/x and g(x) = x^2 on the interval [1,3] b) f(x) = x^3 - 3x^2 + 2x and x-axis on the interval [1,2] c) f(x) = si      Log On


   

Question 1113349: please help

Find the area bounded between
a) f(x) = 1/x and g(x) = x^2 on the interval [1,3]
b) f(x) = x^3 - 3x^2 + 2x and x-axis on the interval [1,2]
c) f(x) = sinx and g(x) = cosx on the interval from 0 to the first intersection point on the positive axis.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
please help
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I am not going to TAKE these integrals for you or instead of you.
I will only EXPLAIN to you how to do it. 

Find the area bounded between 
a)  f(x) = 1/x and g(x) = x^2 on the interval [1,3] 

    The area is equal to the integral of the difference  x%5E2+-+1%2Fx  on the interval [1,3].


graph%28+330%2C+330%2C+-0.5%2C+3.5%2C+-2.5%2C+10.5%2C%0D%0A++++++++++x%5E2%2C+1%2Fx%0D%0A%29


Plot y = x%5E2 (red) and y = 1%2Fx (green)



b)  f(x) = x^3 - 3x^2 + 2x and x-axis on the interval [1,2]

    The area is equal to the integral of  -f(x) = -%28x%5E3+-+3x%5E2+%2B+2x%29  on the interval [1,2].





Plot y = x%5E3+-+3x%5E2+%2B+2x



c)  f(x) = sinx and g(x) = cosx on the interval from 0 to the first intersection point on the positive axis.


    Make a plot.

    Find the intersection point. 

    It is the root of the equation sin(x) = cos(x),  which is tan(x) = 1  or  x = pi%2F4.

    The area is the integral of the difference  cos(x) - sin(x)  from 0 to pi%2F4.