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Calculus and Beyond Homework Help
Integral problem: 1/((x^2)(sqrt(4-x^2)))
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[QUOTE="Palmira, post: 4545339, member: 491700"] [h2]Homework Statement [/h2] ∫ dx/ x[SUP]2[/SUP] (√4-x[SUP]2[/SUP]) [h2]Homework Equations[/h2] x=2sinθ dx=2cosθdx sin[SUP]2[/SUP] θ= (1 + cos (2θ))/2 [h2]The Attempt at a Solution[/h2] First attempt: Plug in the trig sub and get: ∫2cosθdθ/4sin[SUP]2[/SUP]θ2cosθ The two cos θ cancel leaving ∫ dθ/ (4sin[SUP]2[/SUP]θ) Now I replace the sin[SUP]2[/SUP]θ with (1-cos2θ)/2 and get 1/2 ∫dθ/(1-cos2θ) I use u sub with the cos2θ u=2θ du/2=dθ ∫cosudu= sin2θ/2 I plug it back into the original equation 1/2 [ 2/θ-sin2θ]= 1/(θ-2sinθcosθ) I retrieve the x from the original equation to get 4/ arcsin(x/2) -(x)(√(4-x[SUP]2[/SUP])) I may be doing something completely wrong, but I can't figure out where. Any hint on where to find the mistake? I keep practicing trig sub problems and I can not get any right. It might have to do with the derivation of the equations, but I am not sure. [/QUOTE]
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Homework Help
Calculus and Beyond Homework Help
Integral problem: 1/((x^2)(sqrt(4-x^2)))
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