What is the integral of the function f(x) = sin 2x?

To find the integral of the function f(x) = sin 2x, we can use the method of substitution. Here are the steps:

1. Let u = 2x. This means that du/dx = 2 or du = 2dx.

2. Rewrite the integral in terms of u. The integral of sin 2x dx becomes the integral of sin u * (1/2) du.

3. Now, we can integrate sin u with respect to u. The integral of sin u du is -cos u + C, where C is the constant of integration.

4. Substitute 2x back in for u to get the final answer: -1/2 cos 2x + C.

To find the integral of the function f(x) = sin 2x, we can use the method of substitution.

Step 1: Let u = 2x. This means that du/dx = 2 or du = 2dx.

Step 2: Rewrite the integral in terms of u. The integral of sin 2x dx becomes the integral of sin u * (du/2).

Step 3: Integrate sin u * (du/2). The integral of sin u is -cos u, so the integral of sin u * (du/2) is -(1/2)cos u + C, where C is the constant of integration.

Step 4: Substitute u = 2x back into the equation to get the final answer. So, the integral of sin 2x dx is -(1/2)cos 2x + C.