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人気のある微分積分 >

integral from-7 to 7 of sqrt(1+(x)^2)

解

\int_{- 7}^{7} 1 + (x)^{2} d x

解

352 + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52))

+1

十進法表記

52.14159 \dots

解答ステップ

\int_{- 7}^{7} 1 + x^{2} d x

三角関数による置換を適用する

= \int_{- a r c t a n (7)}^{a r c t a n (7)} sec^{3} (u) d u

積分換算を適用する

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (7)}^{a r c t a n (7)} + \frac{1}{2} \cdot \int_{- a r c t a n (7)}^{a r c t a n (7)} sec (u) d u

\int_{- a r c t a n (7)}^{a r c t a n (7)} sec (u) d u = ln (7 + 52) - ln (- 7 + 52)

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (7)}^{a r c t a n (7)} + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52))

簡素化

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (7)}^{a r c t a n (7)} + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52)) : [\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (7)}^{a r c t a n (7)} + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52))

= [\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (7)}^{a r c t a n (7)} + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52))

限度を計算する:

352

= 352 + \frac{1}{2} (ln (7 + 52) - ln (- 7 + 52))

グラフ

人気の例

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