The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We know the area in the polar coordinates is given by:
[tex]\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta[/tex]
We have r = sin2θ
Here the quadrant is not given, so we are assuming we need to find the area in the first quadrant.
Put this value in the above integration and limit 0 to π/2
[tex]\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta[/tex]
After solving the above integration, we get:
[tex]\rm A = \dfrac{\pi}{8}[/tex]
Thus, the area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units
Learn more about integration here:
brainly.com/question/18125359
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