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Question: justify the integral formula with a discussion of areas below...

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(8.5, 10.5) Justify the integral formula with a discussion of areas below the curve, as follows. a. Compute the definite integral using trig sub or the integral tables Va2 t dt b. Draw the Quadrant I graph of the function y a -t2 and show the bounds over which we are integrating assume that the upper bound x is 0 <x<a). Shade the region whose area is the value of the definite integral. c. Divide the area into two smaller areas with a well-chosen line segment. Show that each of the two terms of the definite integral computation represents the area of one of the smaller regions that you created. Use a commonly known area formula for one and the area formula for the arc of a circle from section 10.5 for the other. Justify every element of the definite integral computation as exactly the correct value to describe the area in question.

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