Hello. I wonder if there is a mistake in the 69th session's worked example solution? Integral from (cos(2x))^2 should be x/2 + sin(4x)/8 + c, not x/2 + sin(2x)/4 + c, as it has been written there.

Question

Hello. I wonder if there is a mistake in the 69th session's  worked example solution? Integral from (cos(2x))^2 should be x/2 + sin(4x)/8 + c, not x/2 + sin(2x)/4 + c, as it has been written there.

anonymous · Answer

You can always check the result of an integration by differentiating the result. I'm not sure how you arrived at your solution, but the solution provided in the course materials appears to be correct:$$\frac{ d }{ dx }\left( \frac{ x }{ 2 }+\frac{ \sin 2x }{ 4 }+c \right)=\frac{ 1 }{ 2 }+\frac{ \cos2x }{ 2 }+0=\frac{ 1+\cos2x }{ 2 }=\cos^2x$$

anonymous · Answer

Thanks for the response! When you differentiated above, you got $$cos^{2}x$$But the integrated equation was different - $$\cos^{2}(2x)$$
And I am refering to the equation after the "This is all the side work we need to do here, because we know that" sentence.

anonymous · Answer

Sorry, I thought you were referring to the lecture in clip 1. You're right, the statement in the worked example directly contradicts what we learned in the first lecture clip.