MHB Is Integrating 4cos(3x) the Same as 12cos(x)?

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Integrating 4cos(3x) is not the same as 12cos(x). The integration of trigonometric functions requires careful consideration of their arguments, and you cannot simply multiply the coefficients in this manner. The correct approach involves understanding the integral of cos(3x) and applying the appropriate substitution. The integral of cos(3x) is different from that of cos(x), leading to distinct results. Therefore, the two integrals are not equivalent.
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$ \displaystyle{ \int { 4 \cos(3x) } \,dx } $ .

Hi,

for this problem, is this the same as 12*cos*x?

Thanks,
 
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Hi tmt,

Nope, that's not true. You can't multiply through like that with trig functions. Start with it this way...

What is $$\int \cos(x)dx$$?

What is $$\int \cos(3x)dx$$?
 
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