(1)\int_{0}^{\pi }{|\sqrt{2}sinx+2cosx|dx}=
(2) If \int_{0}^{1}(ax+b)/(x^{2}+3x+2)^{2}dx = 5/2 then find value of a and b
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3 Answers
62\\\int_{0}^{1}\frac{(ax+b)}{(x^2+3x+2)^2}dx=5/2 \\\int_{0}^{1}\frac{(ax+a+b-a)}{(x^2+3x+2)^2}dx=5/2 \\\int_{0}^{1}\frac{(ax+a)}{(x^2+3x+2)^2}dx+\int_0^1\frac{(b-a)}{(x^2+3x+2)^2}dx=5/2 \\\int_{0}^{1}\frac{(ax+a)}{(x+1)^2(x+2)^2}dx+\int_0^1\frac{(b-a)}{(x^2+3x+2)^2}dx=5/2 \\\int_{0}^{1}\frac{(a)}{(x+1)(x+2)^2}dx+\int_0^1\frac{(b-a)}{(x^2+3x+2)^2}dx=5/2
Now try to solve
62for the first one try this "simpler" integral instead..
\int_{0}^{\pi }{|a sinx+b cosx|dx}