What is &#x222B;<!-- ∫ --> &#x2212;<!-- − --> 7 5 </mfrac> <mrow class="MJX-TeXA

dificultehcm

dificultehcm

Answered question

2022-05-02

What is 7 5  sin ( 3 7 t ) d t?

Answer & Explanation

dagars5nx

dagars5nx

Beginner2022-05-03Added 12 answers

Since 7 5 is constant with respect to t, move 7 5 out of the integral.
7 5 sin ( 3 7 t ) d t
Let u=3-7t. Then du=-7dt, so 1 7 d u = d t. Rewrite using u and du.
7 5 sin ( u ) 1 7 d u
Simplify.
7 5 sin ( u ) 7 d u
Since -1 is constant with respect to u, move -1 out of the integral.
7 5 ( sin ( u ) 7 d u )
Simplify.
7 5 sin ( u ) 7 d u
Since 1 7 is constant with respect to u, move 1 7 out of the integral.
7 5 ( 1 7 sin ( u ) d u )
Simplify.
1 5 sin ( u ) d u
The integral of sin ( u ) with respect to u is cos ( u )
1 5 ( cos ( u ) + C )
Simplify.
cos ( u ) 5 + C
Replace all occurrences of u with 3-7t
cos ( 3 7 t ) 5 + C
Reorder terms.
1 5 cos ( 3 7 t ) + C

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