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3 years ago

Evaluate.

Mathematics

1 answer:

madreJ [45]3 years ago

8 0

Answer:

Answer is none of these.

Answer is given below with explanations. 

Step-by-step explanation:

Given that x = -2.5

To find the value of x+13

Ob substituting the value in the given equation 

we get 

= -2.5+13

= 13 - 2.5 (we can also write like this)

= 10.5

Therefore value of x +13 is 10.5

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION. 

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3 years ago

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2 years ago

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Rina8888 [55]

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,

$\int_CPdx+Qdy = \int\int_D(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y})dx dy$

Where C is the curve.

<h3>Calculation:</h3>

The given line integral is

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Where curve C is a circle x² + y² = 4;

Applying green's theorem,

P = 9y³; Q = -9x³

Then,

$\frac{\partial P}{\partial y} = \frac{\partial 9y^3}{\partial y} = 27y^2$

$\frac{\partial Q}{\partial x} = \frac{\partial -9x^3}{\partial x} = 27x^2$

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Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as

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Then the integral becomes

$-27\int\limits^{2\pi}_0\int\limits^2_0r^2. r dr d\theta$

⇒ $-27\int\limits^{2\pi}_0\int\limits^2_0 r^3dr d\theta$

⇒ $-27\int\limits^{2\pi}_0 (r^4/4)|_0^2 d\theta$

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Learn more about green's theorem here:

brainly.com/question/23265902

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