Question

How to solve integral of sin(2x)cos(6x).

A) Use the power rule
B) Apply the chain rule
C) Integration by parts
D) Substitute values

Answer 1

To solve the integral of sin(2x)cos(6x), you can use the method of integration by parts.

Step-by-step explanation:

To solve the integral of sin(2x)cos(6x), we can use the method of integration by parts.

1. Let u = sin(2x) and dv = cos(6x)dx.
2. Calculate du by finding the derivative of u with respect to x. In this case, du = 2cos(2x)dx.
3. Integrate dv to find v. In this case, v = (1/6)sin(6x).
4. Apply the integration by parts formula: ∫u dv = uv - ∫v du.
5. Substitute the values of u, v, du, and dv into the formula. The integral becomes sin(2x)(1/6)sin(6x) - ∫(1/6)sin(6x)(2cos(2x))dx.
6. Simplify and evaluate the remaining integral.

By following these steps, you can solve the integral of sin(2x)cos(6x) using integration by parts.