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" Evaluate "int(0)^( pi)|cos x|dx...

" Evaluate "int_(0)^( pi)|cos x|dx

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Prove that int_(0)^(2a) f(x) dx = 2int_(0)^(a) f(x) dx when f(2a -x) = f(x) and hence evaluate int_(0)^(pi) |cos x| dx .

(a) Prove that int_(0)^(2x) f(x) dx = 2int_(0)^(2x) f(x) dx when f(2a-x) =f(x) and hence evaluate int_(0)^(pi) |cos x| dx . (b) Prove that |{:(-a^(2),ab,ac),(bc,-b^(2),bc),(ca,cb,-c^(2)):}|=4a^(2)b^(2)c^(2) .

Evaluate int _(0)^(pi//2)cos x dx