Question 1180435
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The area of the region under the curve given by the function f(x) = 2x2 + 6 on the interval [0, b] is 36 square units, where b > 0.
The value of b is ?
a. 1
b. 2
c. 3
d. 4
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<pre>
The area under the curve is the integral of the given function from 0 to value of "b".


This integral is equal to  {{{(2/3)b^3 + 6b}}}.


So we need find "b" from equation


    {{{(2/3)b^3 + 6b}}} = 36,

or

    {{{2b^3 + 18b}}} = 108.


The function on the left is monotonically increasing function of "b", 

so if we guess the value, it is the unique solution.


Easy guessing gives  b = 3 as the solution.    <U>ANSWER</U>
</pre>

Solved.