partial fraction integration, please check my working out

**Tweety** · October 8th 2012, 12:27 PM

. What is the exact value of

? Give your answer as a fraction or whole number.

I split the fraction, into two fractions, using partial fractions method, to get

$\int^2_0 \frac{2}{x+4} -\frac{2}{x+5}$

= $ln(x+4) - ln(x+5)$

$ln\frac{x+4}{x+5}$

x=2
x=0

$ln\frac{6}{7} - ln\frac{4}{5}$

$ln \frac{30}{28} = 0.06899$

is the the value of k?

**MarkFL** · October 8th 2012, 12:33 PM

You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.

**Tweety** · October 8th 2012, 12:36 PM

Originally Posted by MarkFL2

You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.

oh yes thank you, so the value of k is 1.071?

**MarkFL** · October 8th 2012, 12:40 PM

No, you wind up with:

$2\ln\left(\frac{15}{14} \right)=\ln(k)$

$\ln\left(\left(\frac{15}{14} \right)^2 \right)=\ln(k)$

And so:

$k=\left(\frac{15}{14} \right)^2=\frac{225}{196}$

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