Originally Posted by

**Seed5813**
1. LarCalcET6 7.1.069.

Find *b* such that the line *y* = *b* divides the region bounded by the graphs of *y* = 25 - *x*^{2} and *y* = 0 into two regions of equal area.

I got:

. . . . .[tex]\displaystyle \int_0^5\, (25\, -\, x^2)\, dx\, =\, \dfrac{250}{3}[/tex]

Then tried to find:

. . . . .[tex]\displaystyle \int_0^b\, (25\, -\, x^2)\, dx\, =\, \dfrac{125}{3}[/tex]

But I get stuck when I try to evaluate it:

. . . . .[tex]\displaystyle 3\int_0^b\, (25\, -\, x^2)\, =\, 125[/tex]

. . . . .[tex]\displaystyle 3\left[\, 25x\, -\, \frac{1}{3}x^3\right]_0^b\, =\, 125[/tex]

. . . . .[tex]\displaystyle 75b\, -\, b^3\, =\, 125[/tex]
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