Physics I / Integrated single-variable calculus problems
Practice question · Select all that apply

Which statements are true for f(x)=sin⁡(x)f(x) = \sin(x)?

Hints
  1. Check each claim against the shape and symmetry of the sine curve.
  2. Across a full period, equal positive and negative areas cancel.
Show the answer
  • A. f is an odd function
  • C. f achieves its maximum value of 1 at x=π/2x = \pi/2
  • D. f′(x)=cos⁡(x)f'(x) = \cos(x)
Why

∫02πsin⁡xdx\int_{0}^{2\pi} \sin x dx = 0, not 1 (symmetric positive and negative areas cancel).

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