# Math Help - integration using partial fraction please can can someone check my working

1. ## integration using partial fraction please can can someone check my working

 . What is the exact value of ? Give your answer as a fraction or whole number

$\int^3_0 \frac{1}{(x+4)(x+5)}$

I have spilt this into partial fractions, and got

$1 = A(x+5) + B(x+4)$

which gives
A=1
B=-1

so I have

$\int^3_0 \frac{1}{x+4} -\frac{1}{x+5}$

so now integrating i get

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

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

I than evaluate this answer from 3-0 and i get $ln\frac{7}{8} - ln\frac{4}{5}$

so I get 0.0936

2. ## Re: integration using partial fraction please can can someone check my working

$\ln(7/8) - \ln(4/5) = \ln(7/8 \div 4/5) = \ln(35/32) \approx 0.0896$

3. ## Re: integration using partial fraction please can can someone check my working

According to your original post, the question was "What is the exact value of k? Give your answer as a fraction or whole number". ln(7/8)- ln(4/5)= ln((7/8)(5/4))= ln(35/32).

Don't forget what the problem asked while doing the work! Your answer to this question should be "k= 35/32".

4. ## Re: integration using partial fraction please can can someone check my working

Tahnk you, but the correct answer is 1.09357, I dont know where i went wrong

5. ## Re: integration using partial fraction please can can someone check my working

Originally Posted by Tweety
Tahnk you, but the correct answer is 1.09357, I dont know where i went wrong
after integration you end up with
$0.0896=\ln(k)$
this should give you k = 1.09357

6. ## Re: integration using partial fraction please can can someone check my working

You might notice that 35/32 = 1.09375. I'll bet the 7 and 5 got reversed somewhere, so HallsofIvy's answer is exactly correct, just in a fraction instead of a decimal.

- Hollywood