![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](/tpl/images/2640/1241/4bd0c.png)
[Left Integral] Integration Rule [Reverse Power Rule]: 
[Right Integral] Trigonometric Integration: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
![\int\limits^\frac{\pi}{2} _\frac{\pi}{3} {x+cos(x)} \, dx\\\\=\frac{1}{2}x^2+sin(x)\Bigr|_{\frac{\pi}{3}}^{\frac{\pi}{2}}\\\\=[\frac{1}{2}(\frac{\pi}{2})^2+sin(\frac{\pi}{2})]-[\frac{1}{2}(\frac{\pi}{3})^2+sin(\frac{\pi}{3})]\\\\=[\frac{1}{2}(\frac{\pi^2}{4})+1]-[\frac{1}{2}(\frac{\pi^2}{9})+\frac{\sqrt{3}}{2}]\\ \\ =\frac{\pi^2}{8}-\frac{\pi^2}{18}+1-\frac{\sqrt{3}}{2}\\ \\ \approx0.8194](/tpl/images/2640/1241/78968.png)
Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx
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Mathematics, 31.01.2022 07:20 victor77
Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx
Answers: 1
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