Evaluate the Double Integral Below $$\int _ { 0 } ^ { \frac { \pi } { 5 } } \int _ { 0 } ^ { 5 } r ^ { 5 } \sin \theta \cos \theta d r d \theta$$

question 70

Multiple Choice

Evaluate the double integral below. $$\int _ { 0 } ^ { \frac { \pi } { 5 } } \int _ { 0 } ^ { 5 } r ^ { 5 } \sin \theta \cos \theta d r d \theta$$

• A) \(\frac { 1202 } { 1203 } \sin \frac { \pi } { 5 }\)
• B) \(\frac { 15625 } { 12 } \sin \frac { \pi } { 5 }\)
• C) \(\frac { 12 } { 15625 } \sin ^ { 2 } \frac { \pi } { 5 }\)
• D) \(\frac { 15625 } { 12 } \sin ^ { 2 } \frac { \pi } { 5 }\)
• E) \(\frac { 1 } { 12 } \sin ^ { 2 } \frac { \pi } { 5 }\)

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Definitions:

Paleolithic Art

The earliest form of prehistoric art, dating back to the Old Stone Age, including cave paintings, carvings, and sculptures made by early humans.

Representation

The use of signs or symbols to stand for objects, values, or concepts in art, literature, and other forms of expression.

Imitation

The action of using someone or something as a model and attempting to replicate or mimic their behavior, appearance, or performance.

Naturalism

The style of painted or sculpted representation based on close observation of the natural world that was at the core of the classical tradition.