Question

F(x,y) = 4 ; r is the region enclosed by the petal of a rose curve r = sin*2theta)

Answer 1

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:

$\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta$

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

$\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta$

After solving the above integration, we get:

$\rm A = \dfrac{\pi}{8}$

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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