#### Seed5813

##### New member

- Joined
- Jan 29, 2018

- Messages
- 24

1. LarCalcET6 7.1.069.

Find

[HR][/HR]

I got:

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

Then tried to find:

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

But I get stuck when I try to evaluate it:

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

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

. . . . .\(\displaystyle \displaystyle 75b\, -\, b^3\, =\, 125\)

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Find

*b*such that the line*y*=*b*divides the region bounded by the graphs of*y*= 25 -*x*[SUP]2[/SUP] and*y*= 0 into two regions of equal area.[HR][/HR]

I got:

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

Then tried to find:

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

But I get stuck when I try to evaluate it:

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

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

. . . . .\(\displaystyle \displaystyle 75b\, -\, b^3\, =\, 125\)

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