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人気のある微分積分 >

integral from 1 to 2 of sqrt(x^2-1)

解

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

解

- \frac{1}{2} ln (2 + 3) + 3

+1

十進法表記

1.07357 \dots

解答ステップ

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

三角関数による置換を適用する

= \int_{0}^{\frac{π}{3}} tan^{2} (u) sec (u) d u

三角関数の公式を使用して書き換える

= \int_{0}^{\frac{π}{3}} (- 1 + sec^{2} (u)) sec (u) d u

拡張

(- 1 + sec^{2} (u)) sec (u) : - sec (u) + sec^{3} (u)

= \int_{0}^{\frac{π}{3}} - sec (u) + sec^{3} (u) d u

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}^{\frac{π}{3}} sec (u) d u + \int_{0}^{\frac{π}{3}} sec^{3} (u) d u

\int_{0}^{\frac{π}{3}} sec (u) d u = ln (2 + 3)

\int_{0}^{\frac{π}{3}} sec^{3} (u) d u = 3 + \frac{1}{2} ln (2 + 3)

= - ln (2 + 3) + 3 + \frac{1}{2} ln (2 + 3)

簡素化

- ln (2 + 3) + 3 + \frac{1}{2} ln (2 + 3) : - \frac{1}{2} ln (2 + 3) + 3

= - \frac{1}{2} ln (2 + 3) + 3

グラフ

人気の例

integral from-3 to 3 of 5-sqrt(9-x^2)

\int_{- 3}^{3} 5 - 9 - x^{2} d x

integral from 0 to 5 of cos(x)

\int_{0}^{5} cos (x) d x

integral from 2 to 3 of 1/(xln^4(x))

\int_{2}^{3} \frac{1}{x ln ^{4} ( x )} d x

integral from 2 to 3 of 2^{2x}

\int_{2}^{3} 2^{2 x} d x

integral from 0 to 7 of xe^{x^2}

\int_{0}^{7} x e^{x^{2}} d x