Find the exact length of the curve. y=x_3/3+1/4x,1\leq x\leq 2

boitshupoO

boitshupoO

Answered question

2021-09-17

Find the exact length of the curve.
y=x33+14x,1x2

Answer & Explanation

tabuordg

tabuordg

Skilled2021-09-18Added 99 answers

The function f(x)=x33+14x is continuous, differentiable on [1,2] and its derivative
f(x)=x214x2 is continuous on [1,2]
so the length L of the curve is given by the formula:
L=121+[x214x2]2dx
therefore,
L=121+[x412+116x4]dx
=12[x4+12+116x4]dx
12[x2+14x2]2dx
12x2+14x2dx
=[13x314x]12
(1323142)(1313141)
=831813+14
=6424324824+624
L=5924

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