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Dmitrij [34]
3 years ago
11

Find the volume of the solid generated by revolving the area bounded by y=x^2 and x-axis from [0,2] around the x-axis

Mathematics
1 answer:
lesya [120]3 years ago
8 0

Answer:  \dfrac{32\pi }{5}\ \text{unit}^3

Step-by-step explanation:

Given

The area is bounded by y=x^2 and x-axis from [0,2]

The volume generated for y=f(x) when rotated about the x-axis in the interval [a,b] is

V=\int_a^b\pi y^2dx

Insert the values

\Rightarrow V=\int_0^2\pi x^4dx\\\\\Rightarrow V=\pi \int_0^2x^4dx\\\\\Rightarrow V=\pi \left[ \dfrac{x^5}{5}\right]_0^2\\\\\Rightarrow V=\dfrac{2^5\pi }{5}\\\\\Rightarrow V=\dfrac{32\pi }{5}\ \text{unit}^3

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