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人気のある微分積分 >

integral from 2 to 8 of sqrt(2x)-x+4

解

\int_{2}^{8} 2 x - x + 4 d x

解

\frac{38}{3}

+1

十進法表記

12.66666 \dots

解答ステップ

\int_{2}^{8} 2 x - x + 4 d x

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= \int_{2}^{8} 2 x - x + 4 d x

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_{2}^{8} 2 x d x - \int_{2}^{8} x d x + \int_{2}^{8} 4 d x

\int_{2}^{8} 2 x d x = \frac{56}{3}

\int_{2}^{8} x d x = 30

\int_{2}^{8} 4 d x = 24

= \frac{56}{3} - 30 + 24

簡素化

\frac{56}{3} - 30 + 24 : \frac{38}{3}

= \frac{38}{3}

グラフ

人気の例

integral from 0 to 4 of 2x-2

\int_{0}^{4} 2 x - 2 d x

integral from 0 to 0 of sqrt(16-x^2)

\int_{0}^{0} 16 - x^{2} d x

integral from-1 to 0 of (3x)/((2+x^2)^4)

\int_{- 1}^{0} \frac{3 x}{( 2 + x ^{2} ) ^{4}} d x

integral from 0 to t of (y(u)-u)

\int_{0}^{t} (y (u) - u) d u

integral from 0 to 9 of pi(2sqrt(x))^2

\int_{0}^{9} π (2 x)^{2} d x