← MATH 01131 · Calculus II
MATH 01131 · Advanced integration
Trig integrals / trig sub
Definition
Trig integrals: use identities (sin²+cos²=1, power-reduction) and strategically save one factor to make a u-sub. Trig sub: replace √(a²−x²), √(a²+x²), √(x²−a²) with a sin/tan/sec substitution.
Read this
For ∫ sinᵐ x cosⁿ x: if one power odd, peel it off for du; if both even, use power-reduction.
Trig sub triangles help convert back to x at the end.
Remember sec/tan and sec/sec patterns for ∫ secⁿ, ∫ tanⁿ.
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Try this
Attempt each problem first, then open the worked solution.
1.Integrate sin³x cos²x and ∫ dx/√(4−x²).