tex]...

June 2022 1 6 Report

Пожалуйста помогите нужно такие примеры научиться решать!!! вычислите: [tex] \sqrt2 \int\limits^ \frac{ \pi }{4} _0 {cosx} \, dx [/tex]

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arsenlevadniy

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$\int\limits^a_b f(x) \, dx = F(x)|^a_b$
$\sqrt2 \int\limits^ \frac{ \pi }{4} _0 {\cos x} \, dx = \sqrt2\sin x|^ \frac{ \pi }{4} _0= \sqrt2(\sin \frac{ \pi }{4} - \sin0)=\sqrt2( \frac{\sqrt2}{2} -0) =\\= \sqrt2\cdot \frac{\sqrt2}{2}=1$

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