(1) The integral is straightforward; <em>x</em> ranges between two constants, and <em>y</em> ranges between two functions of <em>x</em> that don't intersect.
(2) First find where the two curves intersect:
<em>y</em> ² - 4 = -3<em>y</em>
<em>y</em> ² + 3<em>y</em> - 4 = 0
(<em>y</em> + 4) (<em>y</em> - 1) = 0
<em>y</em> = -4, <em>y</em> = 1 → <em>x</em> = 12, <em>x</em> = -3
That is, they intersect at the points (-3, 1) and (12, -4). Since <em>x</em> ranges between two explicit functions of <em>y</em>, you can capture the area with one integral if you integrate with respect to <em>x</em> first:
(3) No special tricks here, <em>x</em> is again bounded between two constants and <em>y</em> between two explicit functions of <em>x</em>.
Epiphany is what can be considered a major realization that can change a persons perspective for better or worse.
Empathy, a skill needed by not just by mankind but all living things, the skill to relate to something’s pain or sorrow.
Sorry that’s all I have
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<u>SINCERITY ACCORDING TO THE INDIVIDUAL LIVING IN A COLLECTIVIST CULTURE:</u>
Collective culture pertains to the culture where more importance is given to the group or collective individuals instead of individualistic importance and goals.
An individual who lives in such collective culture would define sincerity as, a person who is committed to the goal of the community at all times and not letting his individualistic goals take an upward curve or act as a hindrance in achieving his community's goals is attributed as sincere.
