## Integrals IB math HL

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Integrals IB math HL

Integration, Integrals - IB Mathematics HL

How can we find the real number p>1 for which the following definite integral equals to 2?

$\int^p_1(1+\frac{1}{x^2}) \ dx$

Thanks
Brynlee

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm

### Re: Integrals IB math HL

Integration, Integrals - IB Mathematics IB math HL

$\int^p_1(1+\frac{1}{x^2}) \ dx=2 \Rightarrow$

$\Rightarrow \left[ x-\frac{1}{x} \right]_1^p=2$

$\Rightarrow ( p-\frac{1}{p})-( 1-\frac{1}{1}) =2$

$\Rightarrow ( p-\frac{1}{p})=2$

$\Rightarrow p^2-2p-1=0$

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

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: Integrals IB math HL

Thanks miranda!
Brynlee

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm