2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in terms of x and not u the substitulion = X

Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: 1. Calculate the integral 1 y-stnx)dx + cosy dy a) With directly (classical), b) With the Green's…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: 1. What should be A for the path independent of (2,4) xy+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

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Q: Verify Green's Theorem by evaluating both integrals √ y² dx + x² dy = √ √ ( Ox (ON-OM) c for the…

A: Here we have to verify the Green's theorem.

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: To evaluate the integral fx e²dx using integration by parts, the best choices for u and dv are: Oue,…

A: The objective of the question is choose the correct option for integration by parts.

Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

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Q: Q.3 Find the double integral for Sle x² dydx, where R between y = -4/x y = -x and x = -4

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Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: Verify Green's Theorem by evaluating both integrals aN o v² dx + x² dy = / / dA ду ax for the given…

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Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: In Exercises 15–22, graph the integrands and use known area formu- las to evaluate the integrals.…

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

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Q: nnai Question 39 Express the iterated integral [Vz dy dz as a non-iterated (i. single) integral in…

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Q: ii) √²√³ xy² S¹S. -dydx -3 x² +1

A: Evaluate the iterated double integral.        ∫01∫-33xy2x2+1dydx

Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: as a non-iterated (i.e. single) integral in tems of y. Express the iterated integral V dy dz O None…

A: Given integral is  ∫01∫xxdy dxy1-y2 First, We have to reverse the order of integration.

Q: Question included in image

A: The given integral is,

Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: In Vi - dt 3t (b)

A: ln(a)b= b ln(a)

Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [ ] (ON-OM) DA ду for the…

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Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: Calculate the double integral. SSR 6x / 1+xy dA, R = [0, 6] × [0, 1]

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Q: Compute the double integral SS s cat+zy) clxdy R where Ris the aren boun d eel by y--V, y:-x 一<メ4

A: The region of integration is between the given lines where the blue curve is the function y=-x and…

Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1…

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Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

A: The integral is given as Q=∫01∫y2yx-ydx dy. We need to sketch the region of integration of the…

Q: Consider the integral  ∫17⋅x⋅cos(8⋅x) dx Which of the following choices of uu and dvdv are…

A: The given integral is,∫17xcos8x dx

Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: Given integral ∫12∫02x-x21x2+y22dydx. The objective is to evaluate the integral. First we change x…

Q: Verify Green's Theorem by evaluating both integrals ON [ v² dx + x² oy - [√(x 0 ) A dy = dA JR əx ду…

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Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy dA ax ду for the given path. C:…

A: This question is related to vector calculus solved in step 2.

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x du -dp y? dx + (1,2) Moreover…

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Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.