SOLUTION: 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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Question 1180435: 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
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.
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
~~~~~~~~~~~~~ 

The area under the curve is the integral of the given function from 0 to value of "b".


This integral is equal to  .


So we need find "b" from equation


     = 36,

or

     = 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.    ANSWER

Solved.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
The area as a function of b is given by



You want to find such that .
. . . . multiply by to clear fractions
. . . .factor


so, this equation to have one real solution at

The value of is .


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