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Centroid calculation using integrals
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[QUOTE="arhzz, post: 6850108, member: 682934"] Okay here we go $$ x_s1 = \frac{1}{A1} \int_{0}^{1} xf(x)dx $$ With plug in values $$ x_s1 = \frac{1}{1/2} \int_{0}^{1} (1-x) * x dx $$ Multiply the brackets out and get rid of the double fraction $$ 2 * \int_{0}^{1} x^2 - x dx $$ Now solve the Integral, it should be only the power rule so we get $$ 2 * ( \frac{x^2}{2} - \frac{x^3}{3}) $$ And I dont know how to do it in LaTeX but evalute the brackets at 1 and 0. Now I put the bracket term on a common denominator and get this $$ 2*(\frac{3x^2-2x^3}{6}) $$ So now we have to plug in 1 into x and subtract that from plugging 0 into x. If we plug 1 into this we get 1/6, if we plug 0 we get 0 hence we are left with. $$ 2 * \frac{1}{6} $$ and that is 1/3. Okay for xs2 =$$ 1 * \int_{-pi/2}^{0} xcos(x) dx $$ Use partiall integration to solve the integral; I get $$ 1* (xsin(x)+cos(x))$$ and evaluate at -pi/2 and 0. Plug in first 0 than -pi/2 and subract them from each other.We should get $$ 1*(1-\frac{pi}{2} )$$. This is how I did it [/QUOTE]
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Centroid calculation using integrals
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