Cálculos Del Laboratorio # 1.docx

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Cálculos Del Laboratorio ∫ 𝑥 ⅆ𝑥 𝑥2 2 Integrate[𝑥, 𝑥] 𝑥2 2 Integrate[Sin[𝑥], 𝑥] −Cos[𝑥] Integrate[Sqrt[Tan[𝑥]], 𝑥] 1 2√2

(−2ArcTan[1 − √2√Tan[𝑥]] + 2ArcTan[1 + √2√Tan[𝑥]] + Log[1 − √2√Tan[𝑥] + Tan[𝑥]] − Log[1 + √2√Tan[𝑥] + Tan[𝑥]])

Integrate[Exp[𝑛 ∗ 𝑥], 𝑥] ⅇ 𝑛𝑥 𝑛 Integrate[Exp[𝑛 ∗ 𝑥], {𝑥, 0, ∞}] 1 ConditionalExpression[− , Re[𝑛] < 0] 𝑛 FullSimplify[Integrate[Exp[𝑛 ∗ 𝑥], {𝑥, 0, ∞}], 𝑛𝜖Reals𝑛 ≤ 0] 1 ConditionalExpression[− , 𝑛 < 0] 𝑛 FullSimplify[Integrate[Exp[𝑛 ∗ 𝑥], {𝑥, 0, ∞}], 𝑛𝜖Reals&&𝑛 < 0] −

1 𝑛

∫ ∫ ∫ (𝑥 ∗ 𝑦^2 ∗ √𝑧) ⅆ𝑥 ⅆ𝑦 ⅆ𝑧 1 2 3 3⁄2 𝑥 𝑦 𝑧 9 Integrate[Integrate[Integrate[𝑥 ∗ 𝑦^2 ∗ Sqrt[𝑧], 𝑥], 𝑦], 𝑧] 1 2 3 3⁄2 𝑥 𝑦 𝑧 9 Integrate[Integrate[Integrate[𝑥 ∗ 𝑦^2 ∗ Sqrt[𝑧], {𝑥, 0, 𝜋}], {𝑦, 2,7}], {𝑧, 1,15}] 335 (−1 + 15√15)𝜋 2 9 F[x_] = Sin[x] Sin[𝑥]

Plot[𝐹[𝑥], {𝑥, 0,2𝜋}] 1.0

0.5

1

2

3

4

5

6

0.5

1.0

𝑔[x_, y_] = Exp[−(𝑥^2 + 𝑦^2)] ⅇ −𝑥

2 −𝑦 2

Plot3D[𝑔[𝑥, 𝑦], {𝑥, −2,2}, {𝑦, −2,2}]

𝐷1 = {{0,0}, {1,1.2}, {2,3.8}, {3,9.1}, {4,15.5}, {5,25}, {6,35}}

Cálculos hechos en casa 1) Resuelva en mathematica la siguiente integral, asuma que z y r son reales positivos y que z es mayor que r. (sugerencia: vea la pagina 80 del libro: campos electromagneticos R. Wangsness).

(𝑧 − 𝑟 ∗ cosθ) ∗ sinθ FullSimplify[Integrate[ , {𝜃, 0, 𝜋}], 𝑧&&𝑟𝜖Reals&&𝑧 (𝑧^2 + 𝑟^2 − 2 ∗ 𝑧 ∗ 𝑟 ∗ cosθ)^(3⁄2) > 𝑟] (𝑟 2

𝜋sinθ(−cosθ𝑟 + True) − 2cosθ𝑟True + True2 )3⁄2 2) Resuelva en mathematica la siguiente integral, asuma que A y B son reales positivos y que A es mayor que B. (Nota: vea la pagina 81 del libro: Campos Electromagneticos R. Wangsness).

(𝑎 − 𝑏 ∗ cosθ) FullSimplify[Integrate[ , {𝜃, 0, 𝜋}], 𝑎&&𝑏𝜖Reals&&𝑎 > 𝑏] 𝑎^2 + 𝑏^2 − 2 ∗ 𝑎 ∗ 𝑏 ∗ cosθ 𝜋(−𝑏cosθ + True) 𝑏 2 − 2𝑏cosθTrue + True2 3) Haga el grafico, en mathematica, de las siguientes funciones

𝐻[x_, y_] = Sin[Sqrt[𝑥^2 + 𝑦^2]] Sin[√𝑥 2 + 𝑦 2 ] Plot3D[𝐻[𝑥, 𝑦], {𝑥, −2,2}, {𝑦, 0,4}]

𝐽[x_, y_] = Sin[𝑥^2] − Cos[𝑦^3] −Cos[𝑦 3 ] + Sin[𝑥 2 ]

Plot3D[𝐽[𝑥, 𝑦], {𝑥, 0,4}, {𝑦, −2,2}]

4) Grafique las curvas de nivel (lineas equipotenciales) de las siguientes funciones escalares:

𝑦^2 ContourPlot[ , {𝑥, 1,3}, {𝑦, −2,2}] Sqrt[(𝑥 − 2)^2 + 𝑦^2]

𝑥^2 ContourPlot[ , {𝑥, −2,2}, {𝑦, 1,3}] Sqrt[𝑥^2 + (𝑦 − 2)^2]

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