Find the integral of

Wissety52

Wissety52

Answered question

2022-05-03

Find the integral of 1 3 cos ( 4 t + 1 ) with respect to t.

Answer & Explanation

Narissiyks

Narissiyks

Beginner2022-05-04Added 7 answers

Since 1 3 is constant with respect to t, move 1 3 out of the integral.
1 3 cos ( 4 t + 1 ) d t
Let u=4t+1. Then du =4dt, so 1 4 d u = d t. Rewrite using u and du
1 3 cos ( u ) 1 4 d u
Combine cos ( u ) and 1 4
1 3 cos ( u ) 4 d u
Since 1 4 is constant with respect to u, move 1 4 out of the integral.
1 3 ( 1 4 cos ( u ) d u )
Simplify
1 12 cos ( u ) d u
The integral of cos ( u ) with respect to u is sin ( u ).
1 12 ( sin ( u ) + C )
Simplify.
1 12 sin ( u ) + C
Replace all occurrences of u with 4t+1.
1 12 sin ( 4 t + 1 ) + C

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