(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>.

Answer:
The Industrial Revolution changed the way things were made as new machines invented in the 1700s and 1800s meant it was possible to mass produce goods in factories. Starting in Britain and spreading through Europe and North America, a period of rapid social and economic change began, with widespread URBANIZATION.
Explanation:
<h3>#CARRY-ON Learning</h3>