The equations are given whose graphs enclose a region. when the area of the region is 301.5
The given function is f(x) and g(x), we need to calculate the area.
A = ₐ∫ᵇ (f(x) + g(x)) dx
A = ₀∫³ (x² + 15(x + 5)) dx
A = ₀∫³ (x²dx + ₀∫³15(x + 5)) dx
A = (x³/3) + 15x²/2 + 75x
A = ₀[x³/3]³ + ₀[15x²/2 + 75x]³
A = [(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]
A = 27/3 + 15(9/2) + 75(3)
A = 9 + 15(4.5) + 7
A = 76.5 + 225
A = 301.5
Therefore, the equations are given whose graphs enclose a region. when the area of the region is 301.5
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