Calculus › Section I · Integration techniques and improper integrals › Topic I.3
Trigonometric integrals
No basic rule fits ∫sin²x dx: substituting u = sin x would need a spare cos x for du, and there is none. The unlocking tools are not new integration rules at all — they are trigonometric identities. This topic is a strategy lesson: classify the integral by whether its powers are odd or even, then choose the identity that flattens it into pieces you already know.
In this topic
- The identity toolkit
- Odd powers: save one factor
- Even powers: half-angle formulas
- Worked example: mixed powers
- Tangents and secants
- Worked example: a power of tangent
- Applied: why a wall outlet says 120 volts
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP