Assignment 11.1 CENTER OF MASS due 12/31/2012 at 08:00am PST
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1 Assignment. CENTER OF MASS due // at 8:am PST MATH 9B S. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg bounded by the curves y = 4 x and y =. 8/5. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 4.pg bounded by the curves x + y = 6, y =, and x =. /. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 5.pg bounded by the curves y = e x, y =, x =, and x =. /(exp(- (exp(+/4 4. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 6.pg bounded by the curves y = /x, y =, x =, and x =. /ln( /(4*ln( 5. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 7.pg bounded by the curves y = x and y = x. /5 / 6. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 8.pg bounded by the curves y = x + and y = x. / 8/5 7. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 9.pg bounded by the curves y = sin(x, y = cos(x, x =, and x = π/4. (pi*sqrt(-4/(4*(sqrt(- /(4*(sqrt(- Generated by c WeBWorK, Mathematical Association of America
2 Assignment. IMPROPER INTEGRALS due // at 8:am PST MATH 9B S. ( pt Library/UCSB/Stewart5 7 8/Stewart pg Z x 5 dx. ( pt Library/UCSB/Stewart5 7 8/Stewart pg Z x (x + dx /4. ( pt Library/UCSB/Stewart5 7 8/Stewart5 7 8.pg Z e t dt 4. ( pt Library/UCSB/Stewart5 7 8/Stewart5 7 8.pg Z ( v 4 dv 5. ( pt Library/UCSB/Stewart5 7 8/Stewart pg Z z + z + dz -*ln( 6. ( pt Library/UCSB/Stewart5 7 8/Stewart5 7 8.pg 5re r/ dr 9*-5*exp( 7. ( pt Library/UCSB/Stewart5 7 8/Stewart pg Z x x dx 8. ( pt Library/UCSB/Stewart5 7 8/Stewart5 7 8.pg x dx -*pi/ 9. ( pt Library/UCSB/Stewart5 7 8/Stewart pg ln(x dx x -*-4
3 Generated by c WeBWorK, Mathematical Association of America
4 Assignment.4 ARC LENGTH due // at 8:am PST MATH 9B S. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg Use the arc length formula to find the length of the curve y = x, x. You can check your answer by noting the shape of the curve. *sqrt(. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg Find the exact length of the curve 46/ y = (x /, x.. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 4.pg Find the exact length of the curve /48 y = x 6 + x, x. 4. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 5.pg y = + 6x /, x. 64/4*8ˆ(/-/4 5. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 8.pg 6+ln(/4 y = x ln(x 4, x ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg ln(+ˆ(/ y = ln(cos(x, x π/. 7. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg y = ln(x, x. -sqrt(+ln(sqrt(+-/*ln( 8. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg y = cosh(x, x. /*(exp(-/exp( 9. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 5.pg y = e x, x. sqrt(+exp(-sqrt(+ln(sqrt(+exp(---ln(sqrt(-. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 7.pg Which of the following integrals represents the length of the curve y = cos(x, x π? Z π A. + cos (xdx Z π B. + sin (xdx Z π C. sin (xdx. E. F. Z π Z π Z π + sin(xdx + cos(xdx + cos (xdx
5 B. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 8.pg Which of the following integrals represents the length of the curve y = x, x? Z A. + x dx Z B. + (ln x dx Z C. + (ln x dx. E. F. Z Z Z C + x dx + (ln dx + (ln x dx. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg Which of the following integrals represents the length of the curve x 5 + y 6 =? / A. ( + 6x 6 5(5 x dx Z 5 ( 6x / B (5 x dx Z 5 / C. ( + 6x 5 5(5 x dx /. ( + 6x 6 6(5 x dx ( 6x / E (5 x dx Z 5 / F. ( + 6x 5 6(5 x dx B Generated by c WeBWorK, Mathematical Association of America
6 Assignment.5 SURFACE AREA due // at 8:am PST MATH 9B S. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg surface obtained by rotating the curve y = ln(x, x, about the x-axis? Z A. π x + (/x dx B. π x + (/x dx C. π ln(x (/x dx. π x + (/x dx E. π F. π F ln(x + (/xdx ln(x + (/x dx. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg surface obtained by rotating the curve y = sin (x, x π/, about the x-axis? Z π/ A. π sin (x + (sin(xcos(x dx Z π/ B. π sin (x + (sin(x dx C. π. π E. π F. π Z π/ Z π/ Z π/ Z π/ A x + sin(xcos(xdx x + (sin(xcos(x dx x + (sin(xcos(x dx sin (x + (sin(xcos(x dx Z π/4 C. π sec(x + (tan (x dx Z π/4. π sec(x + (sec(xtan(x dx Z π/4 E. π x + (sec(xtan(x dx Z π/4 F. π x + (tan (x dx E 4. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 4.pg surface obtained by rotating the curve y = e x, y, about the y-axis? A. π B. π C. π. π E. π F. π Z F ln(y + (/ydy e y + (/ydy e y + (/y dy y + (/ydy y + (/y dy ln(y + (/y dy 5. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 6.pg 9x = y + 8, x 6, about the x-axis. 49*pi. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg surface obtained by rotating the curve y = sec(x, x π/4, about the y-axis? Z π/4 A. π sec(x + (sec(xtan(x dx Z π/4 B. π x + (sec(xtan(x dx 6. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 7.pg y = x, 4 x 9, about the x-axis. pi/6*(7*sqrt(7-7*sqrt(7
7 7. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 8.pg y = cos(x, x π/6, about the x-axis. pi*(sqrt(/+/4*ln(+sqrt( 8. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 9.pg y = cosh(x, x, about the x-axis. pi*(+/*sinh( 9. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg y = x 6 + x, x, about the x-axis. 6/56*pi. ( pt Library/UCSB/Stewart5 8 /Stewart5 8.pg x = + y, y, about the x-axis. pi/4*(65*sqrt(65-7*sqrt(7. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 4.pg y = x, x, about the y-axis. pi/6*(5*sqrt(5-. ( pt Library/UCSB/Stewart5 8 /Stewart5 8 6.pg x = acosh(y/a, a y a, about the y-axis. *pi*aˆ*(+/*sinh( Generated by c WeBWorK, Mathematical Association of America
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