Volume Of A Solid Of Revolution

Question

Let $$R$$ be the region bounded by the graphs of $$y = x^2$$ and $$y = 2x$$. Which of the following integrals represents the volume of the solid formed by revolving $$R$$ about the $$x$$-axis?

Accepted Answer

$$\pi \displaystyle\int_{0}^{2} (4x^2 - x^4)\, dx$$

Answer

$$\pi \displaystyle\int_{0}^{2} (2x - x^2)^2\, dx$$

Answer

$$\pi \displaystyle\int_{0}^{4} \left(2\sqrt{y} - \sqrt{y}\right)^2\, dy$$

Answer

$$2\pi \displaystyle\int_{0}^{2} x(2x - x^2)\, dx$$

Volume Of A Solid Of Revolution

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