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(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 soil of the region A (given in the attachment) must have coarse grain sand and gravel deposits.
Explanation:
The remaining part of the question is attached here
Solution
Most of the aquifers are recharged by rainfall or either the surface water that penetrates through the soil into the ground and reaches the aquifer. Hence, the soil type in these regions must be permeable. Gravel and coarse sand along with medium seize sand particles have high permeability. Hence, the soil of the region A (given in the attachment) must have coarse grain sand and gravel deposits.
