Question

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answer is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =

Answer 1

Therefore, the solution is:

`\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}`

Explanation:

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

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

Therefore, the solution is:

`\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}`