5. Find the Cartesian equation for the polar curve r = 3 sin 0. (10 points)...

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5. Find the Cartesian equation for the polar curve r = 3 sin 0. (10 points) 1. Consider $ ( +=+=+ 1 ) dx. dx. Compute the exact value of the definite integral. Then use both the Trapezoidal Rule and Simpson's Rule with n = 4 to approximate its value. Round each answer to four decimal places. Then compare each of the results and determine which one is closer to the exact value. Show all your work, be organized, and be complete. (20 points) 2. Find the Cartesian equation for the set of parametric equations x = 2sin()-1, y = 3 cos(t)-2 (10 points) 8. Find the area of the region that is inside the circle r = 3sin(e) and outside the cardioid r=1+sin. (15 points) A= B 9. Find the second derivative of the parametric equations x = 512-61 +4,y=1 +61-1. For which values of t is the curve concave up? (15 points) 1 of 6 6. Find the slope of the tangent line for the polar curve r = 2 sin at 0 = (10 points) 8225906 6 = 11/6 7. Find the area enclosed by three petals of the rose r = 4 sin (50). (10 points) r = y sin sx-o) Find the arc length of the curve represented by x=1+31, y=4+21 for 011. (10 points) 5. Find the Cartesian equation for the polar curve r = 3 sin 0. (10 points) 1. Consider $ ( +=+=+ 1 ) dx. dx. Compute the exact value of the definite integral. Then use both the Trapezoidal Rule and Simpson's Rule with n = 4 to approximate its value. Round each answer to four decimal places. Then compare each of the results and determine which one is closer to the exact value. Show all your work, be organized, and be complete. (20 points) 2. Find the Cartesian equation for the set of parametric equations x = 2sin()-1, y = 3 cos(t)-2 (10 points) 8. Find the area of the region that is inside the circle r = 3sin(e) and outside the cardioid r=1+sin. (15 points) A= B 9. Find the second derivative of the parametric equations x = 512-61 +4,y=1 +61-1. For which values of t is the curve concave up? (15 points) 1 of 6 6. Find the slope of the tangent line for the polar curve r = 2 sin at 0 = (10 points) 8225906 6 = 11/6 7. Find the area enclosed by three petals of the rose r = 4 sin (50). (10 points) r = y sin sx-o) Find the arc length of the curve represented by x=1+31, y=4+21 for 011. (10 points)