Question

The tempetature in degrees Celsius of a thin rectangular metal plate located on the region [0,1]×(1,4) is given by

T(x,y) = (x² + √y ) sin (x² y² ) .Finding the average temperature on the plate exactly is very difficult, but we can find an upper bound for it. (a). Find the area of the plate.

Answer 1

To find the area of the plate described, we multiply the length and width, resulting in 3 square units. This value can be used to further analyze heat conduction on the plate.

Step-by-step explanation:

The student is asking a question related to the concept of heat conduction through materials, which is a topic covered in high school physics courses. The area of the plate is a prerequisite calculation before analyzing heat transfer on the plate. The area of a rectangular plate is given by the product of its length and width. In this case, the dimensions of the region are [0,1] × (1,4), which means the plate has a length of 1 unit (since 0 to 1 is 1 unit) and a width of 3 units (since 1 to 4 is 3 units). Therefore, the area of the plate is simply 1 × 3 = 3 square units.