Question 1113349
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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.


<pre>
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^2 - 1/x}}}  on the interval [1,3].


{{{graph( 330, 330, -0.5, 3.5, -2.5, 10.5,
          x^2, 1/x
)}}}


Plot y = {{{x^2}}} (red) and y = {{{1/x}}} (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) = {{{-(x^3 - 3x^2 + 2x)}}}  on the interval [1,2].


{{{graph( 330, 330, -0.5, 2.5, -3.5, 3.5,
          x^3 - 3x^2 + 2x
)}}}


Plot y = {{{x^3 - 3x^2 + 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/4}}}.

    The area is the integral of the difference  cos(x) - sin(x)  from 0 to {{{pi/4}}}.
</pre>