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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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Answer:
<h3><u>Required Answer</u><u>:</u><u>-</u></h3>Every number raised to a negative exponent will have a value smaller than 1.
- This is False statement
- It will only be negative if the number is negative with an odd exponent.
- what you're actually doing is dividing instead of multiplying.