Calculate the Iterated Integral $$\int _ { 0 } ^ { x } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } 4 y \sin x d z d y d x$$

question 31

Short Answer

Calculate the iterated integral.
$$\int _ { 0 } ^ { x } \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - y ^ { 2 } } } 4 y \sin x d z d y d x$$

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Definitions:

Taste Bud

Sensory organs located on the tongue that are responsible for detecting taste, including sweet, salty, sour, bitter, and umami.

Olfactory Bulb

A part of the brain responsible for processing smell.

Olfactory Stimulus

Any object or substance that triggers a response from the olfactory system, related to the sense of smell.

Amygdala

A section of the brain that is involved in emotions, emotional behavior, and motivation.