How do you integrate ∫sin2xdx.
Step- 1: Assume a variable:
The given integration is,
∫sin2xdx
Let u=2x.
∴du=2dx
⇒dx=du2
Step- 2: Evaluate the integration:
Substituting this in the above equation we get,
I=∫sinudu2
=12∫sinudu
=-12cosu+c ∵∫sinxdx=-cosx,cbetheintegrationconstant
=-12cos2x+c [∵u=2x]
Hence, the required answer is -12cos2x+c.