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人気のある微分積分 >

integral from 0 to 2 of (sin(x)+e^x)

解

\int_{0}^{2} (sin (x) + e^{x}) d x

解

e^{2} - cos (2)

+1

十進法表記

7.80520 \dots

解答ステップ

\int_{0}^{2} sin (x) + e^{x} 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_{0}^{2} sin (x) d x + \int_{0}^{2} e^{x} d x

\int_{0}^{2} sin (x) d x = - cos (2) + 1

\int_{0}^{2} e^{x} d x = e^{2} - 1

= - cos (2) + 1 + e^{2} - 1

簡素化

= e^{2} - cos (2)

グラフ

人気の例

integral of (x^2(x^3-2x+1))

\int (x^{2} (x^{3} - 2 x + 1)) d x

derivative of (8x^2+8x+6/(sqrt(x)))

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{x})

integral of 1/(x^3+x^2)

\int \frac{1}{x ^{3} + x ^{2}} d x

integral of (29x^4+29x^3+2x+1)/(x^2+x)

\int \frac{29 x ^{4} + 29 x ^{3} + 2 x + 1}{x ^{2} + x} d x

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\frac{d}{d x} y = (sin (\frac{x}{2}) - cos (\frac{x}{2}))^{2}