Completing the Square (Trigonometric Substitution) <msqrt> 1 &#x2212;<!-- − -->

Kevin Snyder

Kevin Snyder

Answered question

2022-05-14

Completing the Square (Trigonometric Substitution)
1 49 x 2 d x

Answer & Explanation

HowOPpodopgtk3

HowOPpodopgtk3

Beginner2022-05-15Added 20 answers

Hint: For the integrand 1 49 x 2 , substitute x = sin ( u ) 7 and d x = cos ( u ) 7 d u
Then
1 49 x 2 = 1 sin 2 ( u ) = cos ( u ) .
Therefore
1 49 x 2 d x = 1 7 cos 2 ( u ) d u
where u = sin 1 ( 7 x )
For the integral of u = sin 1 ( 7 x ) use the trigonometric identity
cos 2 ( u ) = 1 2 cos ( 2 u ) + 1 2 .

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