Calculate the Double Integral $$\iint _ { R } x y e ^ { y } d A , R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 3 \}$$

question 16

Short Answer

Calculate the double integral. Round your answer to two decimal places.
$$\iint _ { R } x y e ^ { y } d A , R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 3 \}$$

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Definitions:

Micrometers

Units of length in the metric system equal to one millionth of a meter, commonly used in science and engineering for precise measurements.

μm

Micrometer, a unit of length in the metric system equal to one millionth of a meter, used to measure small distances, such as those in biological cells and structures.

Total Magnification

The combined magnifying power of an optical system, calculated by multiplying the objective lens magnification by the ocular lens magnification.

Ocular Lens

A transparent structure in the eye that, along with the cornea, helps to refract light to be focused on the retina.