Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. x=sqrt(y)-y, 1<=y<=4

bu1tu2t1zt

bu1tu2t1zt

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2022-08-19

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.
x=yy,1y4

Answer & Explanation

Rachael Trevino

Rachael Trevino

Beginner2022-08-20Added 9 answers

Arc Length Formula
If f'(y) is continuous on [a,b], then the length of the curve x=f(y),ayb, is
L=ab1+[f(y)]2 dy 
The length of the curve x=yy,1y4  must be determined. 
f(y)=12y1
Thus
L=141+(12t1)2 dy 
The issues require the use of a calculator.
Using a calculator, i found
L=141+(12y1)2 dy 3.6095
Answer:
L=141+(12y1)2 dy 3.6095

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