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Evaluate the following definite integral correct to three decimal places:

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\\(\\int_\\var{a}^\\var{b}\\var{m}sin(\\var{k}t)cos^\\var{n}(\\var{k}t)dt\\)

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\\(Answer =\\) [[0]]

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\\(\\int_\\var{a}^\\var{b}\\var{m}sin(\\var{k}t)cos^\\var{n}(\\var{k}t)dt\\)

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Let \\(u=cos(\\var{k}t)\\)  \\(\\implies \\frac{du}{dt}=-\\var{k}sin(\\var{k}t)\\)

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\\(-\\frac{1}{\\var{k}sin(\\var{k}t)}du=dt\\)

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\\(\\int_\\var{a}^\\var{b}\\var{m}sin(\\var{k}t)u^\\var{n}\\frac{-1}{\\var{k}sin(\\var{k}t)}du\\)

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\\(=\\int_\\var{a}^\\var{b}-\\frac{\\var{m}}{\\var{k}}u^\\var{n}du\\)

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\\(=-\\frac{\\var{m}}{\\var{k}}\\frac{u^{\\simplify{{n}+1}}}{\\simplify{{n}+1}}\\)

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\\(=-\\frac{\\var{m}}{\\simplify{{k}*({n}+1)}}cos^{\\simplify{{n}+1}}(\\var{k}t)\\Big|_\\var{a}^\\var{b}\\)

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\\(=-\\frac{\\var{m}}{\\simplify{{k}*({n}+1)}}\\left(cos^{\\simplify{{n}+1}}(\\simplify{{k}*{b}})-cos^{\\simplify{{n}+1}}(\\simplify{{k}*{a}})\\right)\\)

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\\(=\\simplify{-{m}/({k}*({n}+1))}*\\left(cos^{\\simplify{{n}+1}}(\\simplify{{k}*{b}})-cos^{\\simplify{{n}+1}}(\\simplify{{k}*{a}})\\right)\\)

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