Please answer quick I will give brainliest to the first answer Mr. Morris is going to save money and replace his sailboat's main
sail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work
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The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.
<h3>What is green's theorem?</h3>The theorem states that,
Where C is the curve.
<h3>Calculation:</h3>The given line integral is
Where curve C is a circle x² + y² = 4;
Applying green's theorem,
P = 9y³; Q = -9x³
Then,
⇒
Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as
0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π
Then the integral becomes
⇒
⇒
⇒
⇒
⇒
⇒ -216π
Therefore, the required value is -216π.
Learn more about green's theorem here:
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