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SOLUTION 4:    If y=3+(4/5)x5/4 for 0x1, then dydx=(4/5)(5/4)x1/4=x1/4 so that ARC=101+(dydx)2 dx =101+(x1/4)2 dx =101+x1/2 dx =101+x dx (Now integrate using the method of "power" u-substitution. Let u=1+x  u2=1+x  x=u21  x=(u21)2=u42u2+1   dx=(4u34u)du  .) =x=1x=0u2(4u34u) du =x=1x=0u(4u34u) du =x=1x=0(4u44u2) du =((4/5)u5(4/3)u3) |x=1x=0 =((4/5)(1+x)5(4/3)(1+x)3) |10 =((4/5)(1+1)5(4/3)(1+1)3)((4/5)(1+0)5(4/3)(1+0)3) =((4/5)(2)5(4/3)(2)3)((4/5)(1)5(4/3)(1)3) =45(42)43(22)(12152015) =(16583)2+815 =(48154015)2+815 =8152+815 =815(2+1)

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