Calculating yA.
Notice;
xA = 4
And y = (16+e^(0.5x))/4
y = ¼(16+e²)
Where y is yA.
Therefore;
Shaded Area as a single fraction is;
Area Rectangle with width 4 units and length ¼(16+e²) units - Area under the curve at x = 0 and x = 4
= (4*¼(16+e²))-((16+0.5e²)-½)
= (16+e²)-16-½(e²)+½
= e²-½(e²)+½
= ½(2e²-e²+1)
= ½(e²+1) square units.
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