UnkleRhaukus
  • UnkleRhaukus
I am having some trouble with a simple integration
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnkleRhaukus
  • UnkleRhaukus
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UnkleRhaukus
  • UnkleRhaukus
\[ \frac{1}{{b-a}^2} \int\limits_{a}^{b}x(b-x)^2 \text{d} x = ... \]
anonymous
  • anonymous
Let's expand the integrand\[\int\limits_a^b x (b^2 - 2xb + x^2) dx = \int\limits b^2x dx - \int\limits 2x^2b dx+ \int\limits x^3 dx\] The limits are the same.

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anonymous
  • anonymous
\[0.5 b^2 x^2 |_a^b - (2/3)bx^3 |_a^b + (1/4)x^4 |_a^b\]
UnkleRhaukus
  • UnkleRhaukus
\[= \frac{1}{(b-a)^2}\left(\left.\frac{b^2x^2}{2}-\frac{2}{3}bx^3+\frac{x^4}{4} \right|_a^b\right)\] \[\]
UnkleRhaukus
  • UnkleRhaukus
then take out the 1/12 ?
UnkleRhaukus
  • UnkleRhaukus
* x^2/12
UnkleRhaukus
  • UnkleRhaukus
my laptop is about to run out of battery thanks for assistance, ill be back tomorrow to work on this

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