To evaluate the indefinite integral ∫ sin(t) cos(t) dt, we can use a u-substitution method. Let’s set:
u = sin(t)
Then, the derivative of u with respect to t is:
du = cos(t) dt
This means we can substitute cos(t) dt with du in our integral:
∫ sin(t) cos(t) dt = ∫ u du
This integral is straightforward to compute:
∫ u du = (u² / 2) + C
Now we substitute back for u:
(sin²(t) / 2) + C
Thus, the result for the indefinite integral is:
Answer: ∫ sin(t) cos(t) dt = (sin²(t) / 2) + C