Problem using both types of substitutions

  • Thread starter Thread starter shreddinglicks
  • Start date Start date
shreddinglicks
Messages
225
Reaction score
7
I've attached the work I have done. Can someone please point me in the right direction? I've tried the problem using both types of substitutions. I keep getting stuck regardless.
 

Attachments

  • SCAN0095.JPG
    SCAN0095.JPG
    23.5 KB · Views: 355
Physics news on Phys.org
I tried reading your attached file. I was not sure what the problem was or what form of the solution is expected.
 
shreddinglicks said:
I've attached the work I have done. Can someone please point me in the right direction? I've tried the problem using both types of substitutions. I keep getting stuck regardless.
Please start a new thread with your problem, using the problem template, which has a section for the problem statement and another section where you show what you've done.
 

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

Find nth derivative of e^m(arcsinx) where x=0
Replies
7
Views
2K
Integrating an inequality for two functions of the same variable
Replies
9
Views
1K
Solving a linear differential equation with constant coefficients
Replies
9
Views
2K
Apostol Problem on ODE applied to Population Growth
Replies
1
Views
1K
Help Understanding A Paper - Brachistochrone With Friction
Replies
2
Views
1K
Integration Substitution Techniques for quadratic expressions under square roots
Replies
9
Views
2K
Solving system of differential equations using matrix exponential
Replies
3
Views
982
Complex Eigenvalues of system of DE
Replies
3
Views
898
Proving function discontinuous at zero
Replies
2
Views
851
Can I Use Substitution to Prove the Residue Theorem Integral?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top