- #1
Killswitch
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I am trying to find the integral to this equation in order to obtain the cross section of a circle that has a radius = 2 and is filled with water up to 1.5.
For some reason, no matter what I do I cannot find the correct solution to this integral. Solving it myself I obtain:
∫√(4-(x-2)^2) dx = (x-2)/2 * √(4-(x-2)^2) + 2arcsin((x-2)/2).
[itex]\int[/itex][itex]\sqrt{4-(x-2)^{2}} dx[/itex] = [itex]((x-2)/2)\sqrt{(4-(x-2)^2)}[/itex] [itex]+ 2arcsin((x-2)/2)[/itex]
Then solving for the definite integral of a=0 and b=1.5 I get: -29.439.
Using Wolfram Alpha I get:
http://www.wolframalpha.com/input/?i=integral+of+(4-(x-2)^2)^0.5
But I cannot solve the definite integral from a=0 and b=1.5 because the equation square roots a negative value.
Using Symbolab I get:
http://symbolab.com/math/solver/step-by-step/calculus/definite-integral-calculator/%5Cint%5Csqrt%7B4-%5Cleft(x-2%5Cright)%5E%7B2%7D%7D
But unfortunately when I solve for the definite integral from a=0 and b=1.5, I get the exact same result I did when I formulated the equation myself.
Can anyone tell me what I am screwing up? I am so confused >.>
For some reason, no matter what I do I cannot find the correct solution to this integral. Solving it myself I obtain:
∫√(4-(x-2)^2) dx = (x-2)/2 * √(4-(x-2)^2) + 2arcsin((x-2)/2).
[itex]\int[/itex][itex]\sqrt{4-(x-2)^{2}} dx[/itex] = [itex]((x-2)/2)\sqrt{(4-(x-2)^2)}[/itex] [itex]+ 2arcsin((x-2)/2)[/itex]
Then solving for the definite integral of a=0 and b=1.5 I get: -29.439.
Using Wolfram Alpha I get:
http://www.wolframalpha.com/input/?i=integral+of+(4-(x-2)^2)^0.5
But I cannot solve the definite integral from a=0 and b=1.5 because the equation square roots a negative value.
Using Symbolab I get:
http://symbolab.com/math/solver/step-by-step/calculus/definite-integral-calculator/%5Cint%5Csqrt%7B4-%5Cleft(x-2%5Cright)%5E%7B2%7D%7D
But unfortunately when I solve for the definite integral from a=0 and b=1.5, I get the exact same result I did when I formulated the equation myself.
Can anyone tell me what I am screwing up? I am so confused >.>
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