60 баллов.................... Created by SweepyLook. algebra-ru

60 баллов...

SweepyLook @SweepyLook

October 2021 1 9 Report

60 баллов...................

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$1)\; \int _0^1(x^2+x)^2dx=\int _0^1(x^4+2x^3+x^2)dx=(\frac{x^5}{5}+\frac{2x^4}{4}+\frac{x^3}{3})|_0^1=\\\\=\frac{1}{5}+\frac{1}{2}+\frac{1}{3}+\frac{6+15+10}{30}=\frac{31}{30}\\\\2)\; \int _0^{\frac{\pi}{2}}(cos^2\frac{x}{2}-sin^2\frac{x}{2})dx=\int _0^{\frac{\pi}{2}}cosx\, dx=sinx|_0^{\frac{\pi}{2}}=\\\\=sin\frac{\pi}{2}-sin0=1\\\\3)\; \int_3^5|x|\, dx=[\, 3 \leq x \leq 5\; \to \; |x|=x\, ]=\\\\=\int _3^5x\, dx=\frac{x^2}{2}|_3^5=\frac{1}{2}(25-9)=8$

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