Integrate the Function F Over the Given Region $f ( x , y ) = y ^ { 2 } e ^ { x ^ { 4 } }$

question 167

Multiple Choice

Integrate the function f over the given region.
- $f ( x , y ) = y ^ { 2 } e ^ { x ^ { 4 } }$ over the triangular region in the first quadrant bounded by the lines $x = y / 2 , x = 1 , y = 0$

• A) \(\frac { 8 } { 3 } ( \mathrm { e } - 1 )\)
• B) \(8 ( e + 1 )\)
• C) \(\frac { 2 } { 3 } ( \mathrm { e } - 1 )\)
• D) \(\frac { 2 } { 3 } \mathrm { e }\)

---

Definitions:

Horizontal Plane

A plane that divides the body into upper and lower parts.

Lymphatic System

A network of tissues and organs that help rid the body of toxins, waste and other unwanted materials, integral to the immune system.

Lymph Nodes

Small, bean-shaped structures in the lymphatic system that act as filters for harmful substances.

Pineal Gland

A small, pinecone-shaped endocrine gland in the brain that produces melatonin, a hormone that regulates sleep patterns.