Compute the area between the curves $y=x^{2}$ and $y=2 x$.

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∻Solution by Steps∻ ‖ step 1 ⋮ To find the area between the curves $y=x^{2}$ and $y=2x$, we set up the integral of the difference between the two functions from the lower bound to the upper bound. ‖ ‖ step 2 ⋮ The points of intersection are found by setting $x^{2}=2x$, which gives us $x=0$ and $x=2$ as the bounds of integration. ‖ ‖ step 3 ⋮ The integral to compute the area is $\int_{0}^{2} (2x - x^{2}) dx$. ‖ ‖ step 4 ⋮ Using the asksia-ll calculator result, we have the integral evaluated from 0 to 2: $\int_{0}^{2} (2x - x^{2}) dx = \frac{4}{3}$. ‖ ∻Answer∻ ⚹ $\frac{4}{3}$ or approximately 1.3333 ⚹ ∻Key Concept∻ ⚹Area between two curves⚹ ∻Explanation∻ ⚹The area between two curves in a given interval is found by integrating the difference of the functions over that interval. The result of the definite integral gives the area.⚹◊What is the process for finding the area between two curves in calculus?⍭ Generate me a similar question◊

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