Lista de Exercícios Resolvidos - Cálculo de Integrais Duplas e Triplas

Exercícios 1 Calcule o valor das integrais a ¹⁴₀²6x² 2x dydx b ₀¹¹²4x³ 9x²y² dydx c ¹²₁²x² y dydx d ₀¹₁² exy dydx e ₀²₀π2 x sen y dydx f π6π2¹⁵ cos y dzcdy g ₀¹₀π y² sen³ x dxd y h ₀¹₀³ ex3y dxd y 2 Calcule o valor das integrais sobre os retângulos R a R xy² x² 1 dA onde R xy 0 x 1 3 y 3 b R 1 x² 1 y² dA onde R xy 0 x 1 0 y 1 Questão 01 Calcule o valor das integrais a ¹⁴₀² 6x² 2x dydx ¹⁴ 46x²2x₀² dx ¹⁴ 26x²2x dx ¹⁴ 12x² 4x dx 4x³ 2x²₁⁴ 256 32 4 2 222 b ₀¹₁² 4x³ 9x² y² dydx ₀¹ 4x³ y 3x² y³₁² dx ₀¹ 8x³ 24x² 4x³ 3x² dx ₀¹ 4x³ 27x² dx x⁴ 9x²₀¹ 1 9 8 c ₁²₁² x² y dydx ₁² x² ln y₁² dx ₁² x² ln 2 x² dx ₁² x² ln 2 dx 0 d ₀¹₁² exy dydx u x y dv dy ₀¹₁² ev du dx ₀¹ exy₁² dx ₀¹ ex2 ex1 dx ₀¹ e³ dx x e³₀¹ e³ e ₀²₀π2 x sen y dydx ₀² x cos y₀π2 dx ₀² x cosπ2 1 x cos 0 dx ₀² x dx x² 2₀² 2 f π6π2¹⁵ cos y dx dy π6π2 x sen y¹⁵ dy π6π2 5 sen y 3 sen y dy π6π2 8 sen y dy 6 cos yπ6π2 6 cosπ2 6 cosπ6 6 3 2 33 Questão 02 calcule o valor das integrais sobre os retângulos R a R x y² x² 3 onde R xy 0 x 1 3 y 3 from 3 to 3 from 0 to 1 x y² x² 3 dx dy u x² 3 du 2x dx dx du 2x from 3 to 3 from 0 to 1 x y² u du 2x dy from 3 to 3 y² 2 ln u from 0 to 1 dy from 3 to 3 y² 2 ln x² 3 from 0 to 1 dy from 3 to 3 y² 2 ln 2 3 dy from 3 to 3 y² 2 0 dy 0 b from 0 to 1 from 0 to 3 ex 3y dx dy u x 3y du dx from 0 to 1 eu du from 0 to 3 dy from 0 to 1 eu from 0 to 3 dy from 0 to 1 ex 3y from 0 to 3 dy from 0 to 1 e3 3y e0 3y dy from 0 to 1 e3 dy y e3 from 0 to 1 e3 a from 0 to π from 0 to π y² sen² x dx dy from 0 to π from 0 to π y² sen² x sen x dx dy from 0 to π y² from 0 to π 1 cos² x sen x dx dy v cos x dv sen x dx dx du sen x from 0 to π y² from 0 to π 1 v² sen x du sen x dy from 0 to π y² from 0 to π v² 1 du dy from 0 to π y² v³ 3 v from 0 to π dy from 0 to π y² cos³ x 3 cos x from 0 to π dy from 0 to π y² cos³ π 3 cos π cos³ 0 3 cos 0 dy from 0 to π y² 13 1 13 1 dy from 0 to π 2 y² dy y³ 3 from 0 to π 2 3 Questão 02 b