To determine
To find:
∫1-sin3tsin2t dt
Answer
-cott+cost+C
Explanation
1) Concept:
Apply the formula of indefinite integral and simplify.
2) Formula:
∫cosec2θ dθ= -cotθ+C
∫sinθ dθ= -cosθ+C
1sin2θ=cosec2θ
3) Calculation:
Consider,
∫1-sin3tsin2t dt
After separating the denominator,
∫1-sin3tsin2t dt=∫(1sin2t dt-sint dt)
The integral can be rewritten as
= ∫cosec2t dt-∫sint dt
By applying the formula of integral, we get
=-cott-(-cost)+C
=-cott+cost+C
Conclusion:
∫1-sin3tsin2t dt= -cott+cost+C