(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the indefinite integral.

[itex]\int\sqrt{28x-x^2} dx[/itex]

3. The attempt at a solution

[itex]\int\sqrt{196-(x-14)^2} dx[/itex]Completing the square

[itex]u=x-14[/itex]

[itex]du=dx[/itex]

[itex]\int\sqrt{196-u^2} du[/itex]u substitution

[itex]u=14sin\theta[/itex]

[itex]du=14cos\theta d\theta[/itex]Trig substitution

[itex]\int\sqrt{196cos^2\theta} 14cos\theta d\theta[/itex]

[itex]\int14cos\theta*14cos\theta d\theta[/itex]

[itex]98\int1+cos2\theta d\theta[/itex]

[itex]98(\theta+sin\theta*cos\theta) + C[/itex]

[itex]98(arcsin(u/14)+(u/14)(\sqrt{196-u^2}/14)[/itex]Solve for Theta

From here I should be able to just sub in for u and arrive at my answer. Unfortunately, it is close but no correct, and I can't see where I'm going wrong. Any ideas?

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# Homework Help: The (im)Possible Integral

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