Thus area now for volume we need the height remember

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Unformatted text preview: basically took height and wrote it as an integral. Volume = where is actually equal to z1 – z2 so we need the negative of the above integral to get the height So brings in the factor in addition to the factor which we had from before. So the volume of a solid in spherical coordinates is represented by: Example: Obtain the formula for the volume of a sphere of radius A using spherical coordinates. Sphere: Example: Summary of Section 13.7 1 Sketch the solid represented by a triple integral that is in spherical coordinates 2 Set up and evaluate a triple integral with spherical coordinates 3 Convert a triple integral from rectangular coordinates to spherical coordinates Section 13.8 Change of Variables in Multiple Integrals In 101B we called this idea substitution for evaluating an integral. Since we have two variables we will be using two variables for our substitution. This idea is thought of as a Transformation from two of the variables, u, v, (uv-plane) to the other two variables x, y, (xy-plane). This is notated by: where . The result of substitution is to simplify the limits and/or the i...
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