Use Green's Theorem to evaluate Se (yæ² – 3) dx + (x³ + 4) dy where Cis shown below. y (-3,3) •(6.3) -3 -2 -1 1 4 5 6. en 2.

Q: Evaluate 8(2x + y) dx + 8xy dy on the given curve from (-1, 2) to (2, 5). (-1,2) (-1,0) X (2,5)…

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Q: 1J, (x) dx I= -J, + J, dx a O dx b O I=J, -2 I=J,+2 dx.c O I= -J, + J dx d O

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Q: tan(v) In(cos(v))dv.

A: Assume lncosv = t Differentiate both sides

Q: Evaluate y sin(xy) dA, where R = [1, 2] × [0, π]. R

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Q: A shopper buys cat food in bags of 3 lbs. Her cat eats 3434 lb each week. How many weeks does one…

A: Given that A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week

Q: dy ? dx If sin(x + y) = xy, what is the expression for cos(x + y) – y x – cos(x + y) (A) cos(r + y)…

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Q: dx 16. S sin Ex di √x u= √√x du= I u 12/12 dx = ५५ -1/2 dx 2 би du YN

A: Solve the integration

Q: i. L x² 8(x – a)dx ii. L,7t? cos t 8(t)dt L,7t? cos(t – 2) 8(t – 2)dt iii. -

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Q: Find dx. Using the substitution u=3 – 2x (3— 2л)5 |

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Q: Can you help me step by step?

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Q: In question (c), please use the computed result to explain why Dx=c is inconsistent

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Q: Which of the following is a 1-form? In the case of a 1-form express it as a linear combination of…

A: A 1-form is a linear function ν: φpℝn→ℝ that is v∈φpℝn Given  φνp=ν·dx1,dx2,...,dxn…

Q: Evaluate: IIncx + y) – dy dx 3 a² \In(2a) – –In(a) – + Ei(-a) – In(a) – In 2 +- Ei(-1) А. B. a*…

A: We are asked to evaluate the double integral:…

Q: Calculate Li eax 1 + ex -dx for 0 < a < 1 using the rectangular contour -R → R → R+ 2πi → -R+ 2πi…

A: If f(z) is regular, except at a finite number of poles within a closed contour C and continuous on…

Q: Please solve. Thank you

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Q: 2. Evaluate a 2а-х У — х dx 4a² + (x + y)² ° using the transformation of coordinates u = x + y, v =…

A: Consider the given information:

Q: The order and degree of the D.E. (²² dx³ a. (3,4) O (a). c. (2,1) O (c). (b). = b. (4,3) dy 1+ is dx…

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Q: In Exercises I and 2, find dy/dx. 1. y = sin (x + 1) x+ cos x x + 1 2. y =

A: As per the company guidelines, I can solve only one question.

Q: dx x dyx+(1+x7y}=12

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Q: For the equation given below, evaluate at the point (1, –2). - el + 18 – e2 = 6x² + 3y². dy at (1,…

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Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions

Q: order and degree

A: Given: dydx73-d3ydx34=0 To find: Order and degree of the given equation.

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: 7 Integrate: 2 -dr ² – 4x + 13 + C

A: let I=∫7x2-4x+13 make the complete square of denominator i.e. (x-2)2+9. using substitution method…

Q: dy Given y- xy2 - x²y=2. Then, at the point (1,2), -is Blark 1 dx

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.