Answer:
33 units²
Step-by-step explanation:
A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...
A = (1/2)(8 + 8.5)(4) = 33
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If you do the integration, it gets a bit messy.
[tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]
The appropriate answer choice is 33 square units.
