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Sagot :
The length of the function x = 2y is 2√5 units
According to the given question.
We have a function
x = 2y
Since, we know that the length of the function in the interval [a, b] is given by
l = [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]
Where, l is the length of the function.
Now, differentiating the given function x = 2y w.r.t y.
Therefore,
dx/dy = 2
So, the length of the given function x = 2y from y = -1 to y = 1 is given by
l = [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]
⇒ l = √5[1 - (-1)]
⇒ l = √5(2)
⇒ l = 2√5
Hence, the length of the function x = 2y is 2√5 units.
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