Find the volume of the solid in the first octant bounded above by z = 9 - x^2, below by z = 0 and...
Question:
Find the volume of the solid in the first octant bounded above by {eq}\displaystyle z=9-x^2 {/eq}, below by {eq}\displaystyle z=0 {/eq} and laterally by {eq}\displaystyle y^2=3x {/eq}.
Solving the Volume of the Region:
Solving the volume of the solid using triple integrals and the formula in setting the integral is the following {eq}\displaystyle V=\int_{x_{1}}^{x_{2}}\int_{y_{1}}^{y_{2}}\int_{z_{1}}^{z_{2}}dzdydx {/eq}. This integral, the limits of integrations are the intervals that described the given solid. The above order of integration is just one of the possible six order of integrations.
Answer and Explanation: 1
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View this answerThe solid bounded by the surfaces is defined in the following intervals,
{eq}\displaystyle 0\leq y\leq 3,\:\frac{y^{2}}{3}\leq x\leq 3,\:0\leq z\leq...
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Volumes of Shapes: Definition & Examples
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Chapter 11 / Lesson 9
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In this lesson, learn the definition of volume and how to find the volume of objects of various shapes. Learn from various solved volume examples.
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