Equation of the curve is;
y = ½(x^(3/2))
It implies;
PR = √(4²+6²)
PR = 2√(13) units
QR = (2√(13))/(cos(90-atan(⅔)))
= 13 units.
Therefore;
Shaded Area is;
(Area under the curve at x = 4 and x = 10) - Area trapezium with parallel sides 4 units and 13 units, and height 6 units.
= 20√(10) - (32/5) - ½*6(4+13)
= 20√(10) - (32/5) - 51
= (100√(10)-287)/5 square units.
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