Q. 61 - Calculus

Question

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane 

$$\begin{gathered} f(x,y)=\sin x\cos y \\ Where R=\left\{\right(x,y\left)\right|0\le x\le \pi ,0\le y\le \pi \} \end{gathered}$$

Step-by-Step Solution

Answer

The value of the integral is 0

Step 1: Given information

We are given a region

$$\begin{gathered} f(x,y)=\sin x\cos y \\ Where R=\left\{\right(x,y\left)\right|0\le x\le \pi ,0\le y\le \pi \} \end{gathered}$$

Step 2: Find the volume

We are given

$$\begin{gathered} {\int }_R\sin x\cos y={\int }_0^{\pi }{\int }_0^{\pi }\sin x\cos ydxdy \\ =[-\cos x\sin y] \\ =0 \end{gathered}$$