show that if k is a positive constant, then the area between the x-axis and one arch of the curve y=sin kx is 2/k

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Mathematics

Cecilia Luna

3 August, 05:16

show that if k is a positive constant, then the area between the x-axis and one arch of the curve y=sin kx is 2/k

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Liberty Ray · Answer 1

Sin (kx) = 0=>x=0,π, ...

∫0πsin (kx) dx=-1/kcos (kx) |π0=-1/k (cos (kπ) - cos (k∗0))

if k is odd then,=-1/k (-1-1) = - 1/k (-2) = 2/k

if k is even then,=-1/k (1-1) = 0