5. Find the area of the region enclosed by the parabolas $y = x^2$ and $y = 2x - x^2$. Make a sketch and shade in the region of interest. Show all work including finding intersection points. (4) 6. Find the area bounded by the curves $y = \sin x$ and $y = \cos x$ from $x = 0$ to $x = \pi$. Make a sketch and shade in the region of interest. Give an exact value answer. (4)
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Setting the two equations equal to each other, we have: x = 2x - x^2 Rearranging the equation, we get: x^2 - x = 0 Factoring out x, we have: x(x - 1) = 0 So, x = 0 or x = 1. Now, let's find the y-values at these intersection points. For x = 0, we have: y = Show more…
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