Evaluate \(\int_0^{\frac{\pi}{2}}sin2xdx\)

  • A 1
  • B zero
  • C -1/2
  • D -1

The correct answer is A. 1

\(\int_0^{\frac{\pi}{2}}\)sin 2x dx = [-1/2cos 2x + C]\(_0^{\frac{\pi}{2}}\)

=[-1/2 cos 2 * π/2 + C] - [-1/2 cos 2 * 0]

= [-1/2 cos π] - [-1/2 cos 0]

= [-1/2x - 1] - [-1/2 * 1]

= 1/2 -(-1/2) = 1/2 + 1/2 = 1

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