At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units
What is integration?
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
#SPJ4
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
