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13 Nov 2019
1) (5 pts) Let a) Compute F"(z) and show that it simplifies to vi (recall that the derivative of arcsin(z) is This means, fr example, that 1-7 dr = F(1)-F(0)-1 arosin(1)-|. But, I also showed in class that this is more easily computed by realizing that -dr is just the area of one quarter of the unit circle b) Use F to compute vT- dr. Give the approximate value of the integral to at least 3 decimal places Also, give the exact value in the form of a sum of two simplified" terms, one of which includes a 3 and the other includes arcsin(0.5). c) Sketch a picture of the unit circle in the first quadrant, and indicate the region whose area is equal to J 1- dr. Draw in the line segment from the origin to the point on the cirele whose r-coordinate is 0.5. Show that this divides the region into two parts whose areas are the two terms from your exact answer to (b).
1) (5 pts) Let a) Compute F"(z) and show that it simplifies to vi (recall that the derivative of arcsin(z) is This means, fr example, that 1-7 dr = F(1)-F(0)-1 arosin(1)-|. But, I also showed in class that this is more easily computed by realizing that -dr is just the area of one quarter of the unit circle b) Use F to compute vT- dr. Give the approximate value of the integral to at least 3 decimal places Also, give the exact value in the form of a sum of two simplified" terms, one of which includes a 3 and the other includes arcsin(0.5). c) Sketch a picture of the unit circle in the first quadrant, and indicate the region whose area is equal to J 1- dr. Draw in the line segment from the origin to the point on the cirele whose r-coordinate is 0.5. Show that this divides the region into two parts whose areas are the two terms from your exact answer to (b).
Reid WolffLv2
17 Jul 2019