Solution Found!
Special case of surface integrals of scalar-valued
Chapter 11, Problem 71AE(choose chapter or problem)
QUESTION:
Suppose that a surface S is defined as \(z=g(x, y)\) on a region R. Show that \(\mathbf{t}_{x} \times \mathbf{t}_{y}=\left(-z_{x},-z_{y}, 1\right)\) and that \(\iint_{S} f(x, y, z) d S=\) \(\iint_{R} f(x, y, z) \sqrt{z_{x}^{2}+z_{y}^{2}+1} d A\).
Questions & Answers
QUESTION:
Suppose that a surface S is defined as \(z=g(x, y)\) on a region R. Show that \(\mathbf{t}_{x} \times \mathbf{t}_{y}=\left(-z_{x},-z_{y}, 1\right)\) and that \(\iint_{S} f(x, y, z) d S=\) \(\iint_{R} f(x, y, z) \sqrt{z_{x}^{2}+z_{y}^{2}+1} d A\).
ANSWER:Solution 71AEStep 1