LAST SUBMISSION Use Simpson\'s Rule with n = 10 to estimate the arc length of th

Question

LAST SUBMISSION

Use Simpson's Rule withn= 10 to estimate the arc length of the curve.

Explanation / Answer

Use Simpson's Rule with n = 10 approximate arc length of the curve y = tan x from 0 -> p/3 y = tan x dy/dx = d/dx tan x = sec² x Arc length is... L = ? v[ 1 + ( dy/dx )² ] dx L = ? v[ 1 + sec^4 x ] dx Apply Simpson's Rule n = 10 0 -> p/3 then ?x = (b - a) / n ?x = (p/3 - 0) / 10 ?x = p/30 L = ? v[ 1 + sec^4 x ] dx L ˜ ( ?x / 3 )[ y(0) + 4y(1) + 2y(2) + 4y(3) + 2y(4) + 4y(5) + 2y(6) + 4y(7) + 2y(8) + 4y(9) + y(10) ] L ˜ ( p/90 )[ y(0) + 4y(1) + 2y(2) + 4y(3) + 2y(4) + 4y(5) + 2y(6) + 4y(7) + 2y(8) + 4y(9) + y(10) ] L ˜ ( p/90 ) x [ 1 v[ 1 + sec^4( 0 )] + 4 v[ 1 + sec^4( p/30 )] + 2 v[ 1 + sec^4( p/15 )] + 4 v[ 1 + sec^4( p/10 )] + 2 v[ 1 + sec^4( 2p/15 )] + 4 v[ 1 + sec^4( p/6 )] + 2 v[ 1 + sec^4( p/5 )] + 4 v[ 1 + sec^4( 7p/30 )] + 2 v[ 1 + sec^4( 4p/15 )] + 4 v[ 1 + sec^4( 3p/10 )] + 1 v[ 1 + sec^4( p/3 )] ] L ˜ ( p/90 ) x [ 1.414213562 + 5.688185418 + 2.893027371 + 5.962940531 + 3.121379013 + 6.666666667 + 3.652050679 + 8.274040244 + 4.894218744 + 12.24921794 + 4.123105626 ] L ˜ ( 0.034906585 ) x ( 58.9390458 ) L ˜ 2.057

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