Question

I NEED HELP FAST, THANKS! :)

Answer 1

33 units²

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.

`\displaystyle(5)/(7)\int_4^8{x^(2/7)}\,dx+(1)/(2)\int_4^8{x^(4/9)}\,dx+\int_4^8{6}\,dx\\\\=\left.\left((5)/(9)x^(9/7)+(9)/(26)x^(13/9)+6x\right)\right|_4^8\approx 33.16`

The appropriate answer choice is 33 square units.