Respuesta :

CastleRook
The area of the resulting figure will be given by:
∫f(x)dx
f(x)=13/2x^3
thus
∫f(x)dx=13/2∫x³dx=13/8[x^4]
integrating over the inerval
13/8(12^4)-13/8(5^4)
=32680+3/8 sq. units
=

The area of resulting surface is [tex]1675.9[/tex] square unit.

Area of surface :

The area of curve is given as,

                               [tex]Area=\int\limits^a_b {y} \, dx[/tex]

Given curve is,   [tex]y=\frac{1}{3}x^{3}[/tex]  and [tex]5 \leq x \leq 12[/tex]

Substitute values in above relation.

                [tex]Area=\frac{1}{3}\int_{5}^{12} x^{3} dx\\\\Area=\frac{1}{3}*(\frac{x^{4} }{4} ) ^{12}_{5}\\ \\Area=\frac{1}{12}*(12^{4}-5^{4} )\\ \\Area=\frac{1}{12}*(20736-625)\\ \\Area=\frac{1}{12}*(20111) =1675.9[/tex]

Learn more about the integration of function here:

https://brainly.com/question/20156869

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