Deriving the Statement on Strang's Linear Algebra Page 230

interested_learner
Messages
210
Reaction score
1
I have a question from Strang's Linear Algebra on page 230. Does anyone know how to derive the attached statement?
 

Attachments

Physics news on Phys.org
When I detatch your document it comes out as gibberish. Could you either post a PDF or type up your question in LaTeX?

Thanks,

Tom
 
Bad first attempt

This was my first attempt. I have my answer though from another post. Thank you. I will use the built in functions after this.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Introduction to Linear Algebra: Solving Real-World Problems
Replies
10
Views
2K
What can we say about the eigenvalues if ##L^2=I##?
Replies
12
Views
2K
Orthogonal Projection Problems?
Replies
5
Views
1K
Linear Algebra How hard is this Linear Algebra textbook?
Replies
17
Views
7K
Help with a Linear Algebra problem please
Replies
3
Views
1K
Solving a Linear Combination Problem
Replies
2
Views
2K
B What unique contributions to math did linear algebra make?
Replies
19
Views
3K
Linearly independent vs dependent functions
Replies
3
Views
1K
Proving statements about matrices | Linear Algebra
Replies
25
Views
3K
I How do Tensors "work" in relation to linear algebraic objects?
Replies
7
Views
248

Hot Threads

Recent Insights

Back
Top