We want to compute the area of the region between the line y = -1 and...

 

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We want to compute the area of the region between the line y = -1 and the parabola y² = 2r + 6 We have two methods to calculate this one. For both methods, start by finding the points of inter- ception and sketching the region. (a) Method 1. Solve for y on the equation y² = 2r+6. You will notice that there are two solutions. Look back at the graph. These correspond to the two branches of the parabola when we consider y as a function of a. Try to decompose your area as the sum of two areas that you can write as integrals. Be careful. (b) Method 2. Think of y as the variable and of r as a function of y. We want to compute the area of the region between the line y = -1 and the parabola y² = 2r + 6 We have two methods to calculate this one. For both methods, start by finding the points of inter- ception and sketching the region. (a) Method 1. Solve for y on the equation y² = 2r+6. You will notice that there are two solutions. Look back at the graph. These correspond to the two branches of the parabola when we consider y as a function of a. Try to decompose your area as the sum of two areas that you can write as integrals. Be careful. (b) Method 2. Think of y as the variable and of r as a function of y.

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