Troubleshooting Homework: Identifying and Addressing Mistakes

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Homework Statement



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Homework Equations



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The Attempt at a Solution



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You're right, it is a conservative field - that's the key to the solution.
I think you're trying to use path independence, which is also key, but try it another way.
you're looking for the integral of F; and F = grad f... well... what's the integral of grad f?
 
Actually, I can't really see a problem. So...am I really just that rusty? What's the answer supposed to be?
 
The only thing you are doing wrong is that you have not finished the problem!

You have (9- 12+ 4)- (1/4+ 1- 1). Okay, what number is that?
 
HallsofIvy said:
The only thing you are doing wrong is that you have not finished the problem!

You have (9- 12+ 4)- (1/4+ 1- 1). Okay, what number is that?

Well, that answer is 3/4, but the answer in the back of the review has -27/4.
 
lzkelley said:
You're right, it is a conservative field - that's the key to the solution.
I think you're trying to use path independence, which is also key, but try it another way.
you're looking for the integral of F; and F = grad f... well... what's the integral of grad f?

I have that written out.
 

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...
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