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人気のある微分積分 >

integral from 0 to 3 of (4t-1)^2

解

\int_{0}^{3} (4 t - 1)^{2} d t

解

111

解答ステップ

\int_{0}^{3} (4 t - 1)^{2} d t

拡張

(4 t - 1)^{2} : 16 t^{2} - 8 t + 1

= \int_{0}^{3} 16 t^{2} - 8 t + 1 d t

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{3} 16 t^{2} d t - \int_{0}^{3} 8 t d t + \int_{0}^{3} 1 d t

\int_{0}^{3} 16 t^{2} d t = 144

\int_{0}^{3} 8 t d t = 36

\int_{0}^{3} 1 d t = 3

= 144 - 36 + 3

簡素化

= 111

グラフ

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\int_{1}^{5} (x^{2} - 1) d x

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