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### Definite Integral question - IB math SL

Posted: Tue Jan 21, 2014 7:32 pm
Integration, Definite Integrals - IB Mathematics IB maths SL

How can we find the real number a>1 for which the following definite integral equals to 4?

$\int^a_1(1+\frac{1}{x^2}) \ dx$

Thanks

### Re: Definite Integral question - IB math SL

Posted: Tue Jan 21, 2014 7:33 pm
Integration - Definite Integral question - IB maths IB mathematics SL

$\int^a_1(1+\frac{1}{x^2}) \ dx=4 \Rightarrow$

$\Rightarrow \left[ x-\frac{1}{x} \right]_1^a=4$

$\Rightarrow ( a-\frac{1}{a})-( 1-\frac{1}{1}) =4$

$\Rightarrow ( a-\frac{1}{a})=4$

$\Rightarrow a^2-4a-1=0$

So, $a=2 + \sqrt{5}$ since $a>1$

Hope these help!!

### Re: Definite Integral question - IB math SL

Posted: Tue Jan 21, 2014 7:34 pm
Thank you!!