Question

(1 point) Consider the area shown below. The curve drawn is x2 + y2 = 2, and we have used the notation Dy for Ay. (Click on the figure for a larger version.) Write a Riemann sum for the area, using the strip shown: Riemann sum= E Now write an integral that gives this area so where a = and b = Finally, calculate the exact area of the region, using your integral area =

Answer 1

ol! Given 2 x²ty²=2 x² + y² =2 2- 2-42 om a=o 2 y²=2 y axis > y=52 According to Riemann Sum Rn = Area = f1g;) by i E √2-y? by ian Riemann Sum= E [12-y ²] Dy The area is given by below 12 A = |√2-y2 dy a=0; b=52 Let's evaluate the integral. note : ſ az x² dx = 2 2 = x² + a sin' (N/A) 52 ve Area= s ra-yr dy - [ 14 12 y + 2 / 2 sin" (8%), sim co]-0+ siūlon] 12 / 2-2 + Sin (1) = - (0+ T2)- al "Exact Area= Ed 2

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