What is the arc length of f ( x ) = x sin &#x2061;<!-- ⁡ --> x &#x2212;<!-- − -

vaganzahi

vaganzahi

Answered question

2022-05-20

What is the arc length of f ( x ) = x sin x cos 2 x on x [ 0 , π ]?

Answer & Explanation

Meadow Knox

Meadow Knox

Beginner2022-05-21Added 12 answers

The arc length s of a function f(x) on x [ a , b ] is given by
s = a b 1 + ( f ( x ) ) 2 d x
Here, f ( x ) = x sin x cos 2 x so f ( x ) = sin x + x cos x + 2 cos x sin x
Then, the arc length in question is given by:
s = 0 π 1 + ( sin x + x cos x + 2 cos x sin x ) 2 d x 6.4705

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