Integrate sinx . cosx
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Step-by-step explanation:
Thus, sin(x)cos(x)=sin(2x)2 . ∫sin(x)cos(x)dx=∫sin(2x)2dx=12∫sin(2x)dx. From here, let u=2x so that du=2dx . =14∫sin(2x)(2)dx=14∫sin(u)du=−14cos(u)+C=−14cos(2x)+C. You can also show that this is equivalent to the other two answers using the identity cos(2x)=cos2(x)−sin2(x) .
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