Calculate the volume of the solid formed by rotating the area between $y = x^2$ and $y = 0$ around the x-axis from $x = 0$ to $x = 1$.

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∻Solution by Steps∻ ‖ step 1 ⋮ To find the volume of the solid formed by rotating the area between $y = x^2$ and $y = 0$ around the x-axis, we use the disk method. ‖ ‖ step 2 ⋮ The volume $V$ of the solid is given by the integral $V = \int_{a}^{b} \pi r^2 dx$, where $r$ is the radius of the disk at a given $x$, which is $y = x^2$ in this case. ‖ ‖ step 3 ⋮ Substituting $y = x^2$ into the formula for volume, we get $V = \int_{0}^{1} \pi (x^2)^2 dx = \int_{0}^{1} \pi x^4 dx$. ‖ ‖ step 4 ⋮ Using the asksia-ll calculator result, we have $\int_{0}^{1} \pi x^4 dx = \frac{\pi x^5}{5} \Big|_0^1$. ‖ ‖ step 5 ⋮ Evaluating the integral from $0$ to $1$, we get $\frac{\pi (1)^5}{5} - \frac{\pi (0)^5}{5} = \frac{\pi}{5}$. ‖ ∻Answer∻ ⚹ The volume of the solid is $\frac{\pi}{5}$ cubic units. ⚹ ∻Key Concept∻ ⚹Disk Method for Volume⚹ ∻Explanation∻ ⚹The disk method involves integrating the area of circular disks along the axis of revolution to find the volume of the solid formed.⚹◊What is the formula for calculating the volume of a solid formed by rotating a given region around the x-axis?⍭ Generate me a similar question◊

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