Question

Find the length of the function over the given interval. y = 3x from x = 0 to x = 2

Answer 1

The length of the function y = 3x over the given interval [0, 2] is 3.2 units

For given question,

We have been given a function  y = 3x

We need to find the length of the function on the interval x = 0 to x = 2.

Let f(x) = 3x where f(x) = y

We have  f'(x) = 3,  so  [f'(x)]² = 9.  

Then the arc length is given by,

$\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2$

This means, the arc length is 3.2 units.

Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units

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