Math 202-oo by Set-up two integral (method Assignment #5 Due on July 11 N. 2016
ID: 2878387 • Letter: M
Question
Math 202-oo by Set-up two integral (method Assignment #5 Due on July 11 N. 2016 2. the curves y-e of washers and method of shells) for the volume enerated by rotating the by the two integrals 0, z 0, and 1 about the y-axis. Use one of the integrals to evaluate the volume. z (method of washers and method of shells) for the volume generated rotating the region bounded (y 2)2, and 2 about the a axis. Use one of the integrals evaluate the volume. by the c two integ (method of washers and method of shells) for the volume obtained by rotating the region bounded y 4ar and y 3 about the line z 1. Use one of the integrals to evaluate the volume. R2 4. et-up two integrals (method of washers and method of volume of the Torus obtained by rotating the circle (r (y 1)2 3 about the line z shells) for the 5. 1. se one of the integrals to evaluate the volume Find the length of the arc of the parabola y from (0, o to (t, 6)Set-up and evaluate an integral for the arc-length v from the polnt to the point (t,t. of the curve 7. Find the approximation Sho for the arc length of the curve v (ra) from r 1 to 5. Find the actual arc-length. How large does n need to be so that the approximation Sn to the arc length is accurate to within 10 3? 8. Find the 9. The line y 3 cuts the circumference of the circle (z 1)2 (y-2)2 2 into two parts. Set-up and evaluate an integral for the length of the smaller part. 10. Find the arc-length of the curve y ln(cos(r) from r 0 to z 7.4. 11. Find the arc-length of the curve y vr from r 0 to z 4. 12 set-up and evaluate an integral for the perimeter of the ellipse (z +12 (y 22 -1Explanation / Answer
6) given curve y =1/x
differentiate with respect to x
dy/dx =-1/x2
ds=[1+(dy/dx)2] dx
ds=[1+(-1/x2)2] dx
ds=[1+(1/x4)] dx
ds=[(1+x4)/x4] dx
arclength S=[1 to t][(1+x4)/x4] dx
arclength S=[1 to t][(1+x4)/x4] dx