The length of the curve r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have:
[tex]\rm r=\sqrt{(1 +cos 2 \theta)}[/tex]
[tex]\rm r=\sqrt{2cos^2 \dfrac{2 \theta}{2}[/tex]
[tex]\rm r = \sqrt{2}cos\theta[/tex]
[tex]\rm \dfrac{dr}{d\theta}= -\sqrt{2}sin\theta[/tex]
Length:
[tex]\rm L = \int\limits^{\pi\sqrt2}_0 {\sqrt{r^2+(\dfrac{dr}{d\theta}})^2} \, d\theta[/tex]
After the value of r and dr/dθ and solve the definite integral, we will get:
L = 2π
Thus, the length of the curve r=√(1+cos 2θ) is 2π after integrating over the limit 0 to π√2
Learn more about integration here:
brainly.com/question/18125359
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