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Reil [10]
3 years ago
15

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answ

er is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =
Mathematics
1 answer:
tankabanditka [31]3 years ago
6 0

Answer:

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

Step-by-step explanation:

We calculate the given integral.  We use the substitution t = 7x.

\int \sin 7x\, dx=\begin{vmatrix} 7x=t\\ 7\, dx=dt\\ dx=\frac{dt}{7} \end{vmatrix}\\\\=\int \sin t \cdot \frac{1}{7}\, dt\\\\=\frac{1}{7}\cdot (-\cos t)\\\\=-\frac{\cos 7x}{7}

Therefore, the solution is:

\boxed{\int \sin 7x\, dx=-\frac{\cos 7x}{7}}

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