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人気のある微分積分 >

integral from 5 to 6 of 2log_{10}(x)

解

\int_{5}^{6} 2 lo g_{10} (x) d x

解

\frac{2 ( 6 ln ( 6 ) - 1 - 5 ln ( 5 ) )}{ln ( 10 )}

+1

十進法表記

1.47952 \dots

解答ステップ

\int_{5}^{6} 2 lo g_{10} (x) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{5}^{6} lo g_{10} (x) d x

部分積分を適用する

= 2 [x lo g_{10} (x) - \int \frac{1}{ln ( 10 )} d x]_{5}^{6}

\int \frac{1}{ln ( 10 )} d x = \frac{1}{ln ( 10 )} x

= 2 [x lo g_{10} (x) - \frac{1}{ln ( 10 )} x]_{5}^{6}

結合

x lo g_{10} (x) - \frac{1}{ln ( 10 )} x : \frac{- x + x ln ( x )}{ln ( 10 )}

= 2 [\frac{- x + x ln ( x )}{ln ( 10 )}]_{5}^{6}

限度を計算する:

\frac{6 ln ( 6 ) - 1 - 5 ln ( 5 )}{ln ( 10 )}

= 2 \cdot \frac{6 ln ( 6 ) - 1 - 5 ln ( 5 )}{ln ( 10 )}

簡素化

= \frac{2 ( 6 ln ( 6 ) - 1 - 5 ln ( 5 ) )}{ln ( 10 )}

グラフ

人気の例

integral from 1 to 10 of x^2-x

\int_{1}^{10} x^{2} - x d x

integral from 0 to 9 of sqrt(8t)

\int_{0}^{9} 8 t d t

integral from 0 to 1 of ln(x)x

\int_{0}^{1} ln (x) x d x

integral from 2 to 6 of 7

\int_{2}^{6} 7 d x

integral from 1 to 5 of (ln(r))/(r^2)

\int_{1}^{5} \frac{ln ( r )}{r ^{2}} d r