Mathematics Logic & Set Applications, Mathematics

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Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w →                                                       (cu → ) * v → =

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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1

Percentage, A person spent 12.5% of his money and then rs.1600 and then 40%...

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from 0->1: Int sqrt(1-x^2) Solution) I=∫sqrt(1-x 2 )dx = sqrt(1-x 2 )∫dx - ∫{(-2x)/2sqrt(1-x 2 )}∫dx ---->(INTEGRATION BY PARTS)        = x√(1-x 2 ) - ∫-x 2 /√(1-x 2 ) Let

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