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

rigliztetbf

rigliztetbf

Answered question

2022-06-21

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

Answer & Explanation

g2joey15

g2joey15

Beginner2022-06-22Added 21 answers

Arc length S = 0 π 1 + ( y ) 2 d x
y = sin x 2 sin x cos x
S = 0 π 1 + ( sin x 2 sin x cos x ) 2 d x
= 0 π 1 + sin 2 x + 4 sin 2 x cos 2 x + 4 sin 2 x cos x d x
= 0 π 1 + sin 2 x + sin 2 2 x + 2 sin 2 x sin x d x
That doesn't simplify easily so computer solution is:
S=4.28154

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