[tex] \displaystyle 1) \:\int\limits^{2\pi}_ \frac{\pi}{6} \cos x\, dx = \boldsymbol{ \sin x\bigg |^{2\pi}_ \frac{\pi}{6} = \sin2\pi - \sin\frac{\pi}{6} = 0-\frac{1}{2}= - \frac{1}{2} } \\ [/tex]
[tex] 2) \: \displaystyle \int\limits^1_ {-2} (4x - 1)\, dx = \boldsymbol{\bigg(\frac{4x^2}{2}- 1\bigg)\, dx = 2x^2 -x \bigg |^1_{ - 2} = (2\,*\,1^2 - 1)- (2\,*\,( - 2)^2-(-2))= 1-10 = -9} \\ [/tex]
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[tex] \displaystyle 1) \:\int\limits^{2\pi}_ \frac{\pi}{6} \cos x\, dx = \boldsymbol{ \sin x\bigg |^{2\pi}_ \frac{\pi}{6} = \sin2\pi - \sin\frac{\pi}{6} = 0-\frac{1}{2}= - \frac{1}{2} } \\ [/tex]
[tex] 2) \: \displaystyle \int\limits^1_ {-2} (4x - 1)\, dx = \boldsymbol{\bigg(\frac{4x^2}{2}- 1\bigg)\, dx = 2x^2 -x \bigg |^1_{ - 2} = (2\,*\,1^2 - 1)- (2\,*\,( - 2)^2-(-2))= 1-10 = -9} \\ [/tex]