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charle [14.2K]
3 years ago
15

Use limits to find the area of the region bounded by the graph f(x)=4-2x^3 , the x-axis , and the vertical lines x=0 and x=1

Mathematics
1 answer:
gtnhenbr [62]3 years ago
3 0

Answer:

\frac{7}{2} square units.

Step-by-step explanation:

We have to use limits to find the area of the region bounded by the graph f(x) = 4 - 2x^{3} , the x-axis, and the vertical lines x=0 and x=1.

So, the area will be

A = \int\limits^1_0 {(4 - 2x^{3})} \, dx

= [4x - \frac{x^{4}}{2} ]^{1} _{0}

= 4 - \frac{1}{2}

= \frac{7}{2} square units. (Answer)

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