{"id":137,"date":"2021-07-30T17:19:40","date_gmt":"2021-07-30T17:19:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/?post_type=chapter&p=137"},"modified":"2022-11-01T04:25:25","modified_gmt":"2022-11-01T04:25:25","slug":"introduction-to-triple-integrals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/introduction-to-triple-integrals\/","title":{"raw":"Introduction to Triple Integrals","rendered":"Introduction to Triple Integrals"},"content":{"raw":"In\u00a0Double Integrals over Rectangular Regions<\/em>, we discussed the double integral of a function [latex]f(x,y)[\/latex]\u00a0of two variables over a rectangular region in the plane. In this section we define the triple integral of a function [latex]f(x,y,z)[\/latex]\u00a0of three variables over a rectangular solid box in space, [latex]\\mathbb{R}^{3}[\/latex]. Later in this section we extend the definition to more general regions in\u00a0[latex]\\mathbb{R}^{3}[\/latex].","rendered":"

In\u00a0Double Integrals over Rectangular Regions<\/em>, we discussed the double integral of a function [latex]f(x,y)[\/latex]\u00a0of two variables over a rectangular region in the plane. In this section we define the triple integral of a function [latex]f(x,y,z)[\/latex]\u00a0of three variables over a rectangular solid box in space, [latex]\\mathbb{R}^{3}[\/latex]. Later in this section we extend the definition to more general regions in\u00a0[latex]\\mathbb{R}^{3}[\/latex].<\/p>\n\n\t\t\t

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