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insens350 [35]
3 years ago
8

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 &

gt; 0.
What is the value of b?

Mathematics
2 answers:
choli [55]3 years ago
8 0

The area as a function of b is given by

a(b)=\int\limits^b_0 {(2x^2+6)} \, dx =\frac{2}{3}b^3+6b


You want to find b such that a(b) = 36.

... (2/3)b^3 +6b = 36

... b^3 +9b -54 = 0 . . . . multiply by 3/2 to clear fractions


A graphing calculator shows this equation to have one real solution at b=3.


The value of b is 3.

Goshia [24]3 years ago
8 0

Answer:

3

Step-by-step explanation:

Plato

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