Let W be the region bounded by z = 36 - y^2, y = 6x^2, and the plane z = 0. Calculate the exact...
Question:
Let W be the region bounded by {eq}z = 36 - y^2, y = 6x^2 {/eq}, and the plane {eq}z = 0 {/eq}. Calculate the exact volume of W as a triple integral in the order dz dy dx.
Calculating volume of a solid using integrals
The volume of a solid in three-dimensional space can be found using a triple integral. A triple integral is evaluated as an iterated integral with limits for each variable.
Let {eq}S {/eq} be a solid in three-dimensional space. Then the volume of the solid can be found by integrating the infinitesimal element {eq}dV {/eq} as: $$\begin{align*} V = \iiint_S dx dy dz \end{align*} $$
Answer and Explanation: 1
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Evaluating Definite Integrals Using the Fundamental Theorem
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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.
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