- #1
carlosgrahm
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How do you integrate
xsinxcosxdx
xsinxcosxdx
The formula for integrating xsinxcosxdx is ∫xsinxcosxdx = ½ [x^2sin2x - ∫sin2xdx].
To solve the integral of xsinxcosxdx, you can use the substitution method by letting u = sinx and du = cosxdx. This will result in the integral becoming ∫xsinxcosxdx = ∫usinu du. You can then use integration by parts to solve the remaining integral.
No, the integral of xsinxcosxdx cannot be simplified further. It is considered a "trigonometric" integral and does not have a simple solution like other integrals.
The limits of integration for the integral of xsinxcosxdx depend on the specific problem given. Typically, you will be given specific values for x or u to plug into the integral after solving it.
Yes, the substitution method and integration by parts are the most commonly used methods to solve the integral of xsinxcosxdx. However, the specific method used may vary depending on the given problem.