Question

Question: To find: The formula offor \(y = h(x,z)\).

Short answer

A surface integral is a surface integration generalisation of multiple integrals. It can be thought of as the line integral's double integral equivalent. It is possible to integrate a scalar field or a vector field over a surface.

Given data:

\(y = h(x,z)(1)\)

Formula used:

Step-by-step solution

Concept of Surface Integral and Formula Used.

A surface integral is a surface integration generalisation of multiple integrals. It can be thought of as the line integral's double integral equivalent. It is possible to integrate a scalar field or a vector field over a surface.

Given data:

\(y = h(x,z)(1)\)

Formula used:

Calculate the Surface Integral.

If \(S\) is \(y = h(x,z)\), then the level surface \(S\) is \(f(x,y,z) = y - h(x,z) = 0\).

Consider\({\rm{F}}({\rm{h}}(x,z)) = P{\rm{i}} + Q{\rm{j}} + R{\rm{k}}\).

Modify equation (2).

Substitute \(P{\rm{i}} + Q{\rm{j}} + R{\rm{k}}\) for \({\rm{F}}({\rm{h}}(x,z))\),