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

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:

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