Mathematics, 30.07.2019 19:50, Chapo3760
If m β€ f(x) β€ m for a β€ x β€ b, where m is the absolute minimum and m is the absolute maximum of f on the interval [a, b], then m(b β a.β€ b f(x) dx a β€ m(b β a). use this property to estimate the value of the integral. 6Ο (2x β 4 sin(x)) dx 5Ο
Answers: 1
![\text{If } m\leq f(x)\leq M\text{ over the interval }[a,b] \text{ then}\\m(b-a)\leq\int_a^bf(x)dx\leq M(b-a)\\\text{The given function is the following:}\\f(x)=2x-4sin(x)\text{over the interval }[5\pi,6\pi ]\\\text{Minimum of the function over the above interval: } m=2(5\pi+\frac{\pi}{2})-4\\\text{Maximum: }M=10\pi\\\text{The integral I we are looking for is in the interval:}\\\pi m\leq I\leq \pi M](/tpl/images/0151/6778/d919b.png)
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If m β€ f(x) β€ m for a β€ x β€ b, where m is the absolute minimum and m is the absolute maximum of f on...
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