Calculus – Integration – Fixed
Compute the integral
∫ from -π to π of (3 + 2 sin x + 3 cos x)(1 + 4 sin x) dxPick ONE option:
- 7π
- 8π
- 14π
- 16π
This question tests definite integration and symmetry properties of trigonometric functions. After expanding the integrand, most terms vanish on the symmetric interval [-π, π] because odd functions integrate to zero there. The key is to simplify the expression first, then evaluate only the terms that contribute to the final value.
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