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integration of square root of a 2 x 2 dx
integration of square root of a 2 x 2 dx
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Integration Of 1 sqrt a 2 x 2 dx Shortcut YouTube
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Integration Of Sqrt x 2 a 2 dx YouTube
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Use the identity cosh2t 1 2 1 cosh2t to get a a 2 1 cosh2t dt a a 2 t sinh2t 2 C If we go back to x we get a a 2 arcsinh x a sinh2arcsinh x a 2 This can be further simplified using the identities sinh2t 2sinhtcosht and cosharcsinh t Answer The integration of square root of a 2 x 2 is equal to a 2 x 2 dx x a 2 x 2 2 a 2 2 sin 1 x a C where C is an integration constant
Integration of square root of a 2 x 2 dx Is there any way to compute the integral begin equation int a a sqrt R 2 x 2 mathrm d x qquad 0
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Integration Of Square Root Of a 2 X 2 dx YouTube
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Integral Of Sqrt a 2 x 2
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Solution Let us put x asin Then we have dx acos d and a2 x2 a2 1 sin2 a2cos2 Explanation For the integral involving the root x2 a2 we use the substitution x asec dx asec tan d So we get a sec tan a2 sec2 1 a sec d Recalling the identity sec2 1 tan2 we get atan tan2 atan2 d To integrate this we ll use the identity tan2 sec2 1 again
Perhaps the simplest is to write ln x a x2 a2 1 C ln x a x2 a2 a C ln x x2 a2 a C ln x x2 a2 lna C But assuming that a is a constant lna is a constant so we can let it be absorbed by the C Indefinite Integrals of Form Sqrt x 2 a 2 In calculus an antiderivative primitive or indefinite integral of a function f is a function F whose derivative is equal to f i e F f The process of solving for antiderivatives is antidifferentiation or indefinite integration Antiderivatives are related to definite integrals through
Question Video Finding The Integration Of A Function Involving A Root
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integration of square root of a 2 x 2 dx - Integration of square root of a 2 x 2 dx