6.6-bo'lim : Ish
1. \(F\left( x \right) = {x^2} - \cos \left( {3x} \right) + 2\), \(x\) kuchi metrlarda, jismga ta'sir qiladi. Ob'ektni \(x = 3\) dan \(x = 7\) ga ko'chirish uchun qanday ish kerak?
Yechim
Bu muammo uchun haqiqatan ham unchalik ko'p narsa yo'q. Bizga integral (\(x = 3\) va \(x = 7\)) uchun kuch funksiyasi va chegaralari berilgan va shuning uchun biz qilishimiz kerak bo'lgan narsa ish uchun integralni yozish va uni baholashdir.
\[\begin{align*}W & = \int_{3}^{7}{{{x^2} - \cos \left( {3x} \right) + 2\,dx}}\\ & = \left. {\left( {\frac{1}{3}{x^3} - \frac{1}{3}\sin \left( {3x} \right) + 2x} \right)} \right|_3^7 = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{3}\left( {340 + \sin \left( 9 \right) - \sin \left( {21} \right)} \right) = 113.1918}}\end{align*}\]