1 dA, where R is the union of both regions bounded by the functions y = sin(3x) x2 + y2 + 4 and y = arctan(x).

Q: QUESTION 6. Use an appropriate change of variable to evaluate the double integral: dA, y+x, COS…

A: Given:- where R is in the first quadrant and bounded by the lines x+y=1 and x + y=2.  To find:- Use…

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

A:

Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: dy sin(x) for y = 1-cos(x) dx 1- Find 2- Find the integral " sin(x)cos°(x)dx

A:

Q: Evaluate the iterated integral. 1/4 y cos(x) dy dx

A:

Q: Evaluate the integral / (2x + 15y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

A:

Q: The integral that represents the arc-length of the curve y = In x, x E [2,3] is: A) 3 Vx2+1 dx. B)…

A: Please refer to the image below

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

Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: 5. Find fSp(x + y)² dx dy, wh- region in Fig. 17.2.12. y = x

A: Answer is 7/12

Q: dy at x = 0 where y dx arctan(0.1arcsin(x)) + x² + 3x. Find

A:

Q: Evaluate the iterated integral.

A: For iterated integrals of the form ∫ab∫cdf(x)g(y)dydx. They can be simplified to ∫abf(x)d∫cdg(x)dx.…

Q: Evaluate the double integral: sin(y) /y³ dy dx.

A: Change the order of integration to simplify the integral .               Disclaimer: Since you have…

Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: evaluate the iterated integral

A: Iterated integral is integral over several variables such that only one variable is integrated over…

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.

Q: Evaluate the integral | (6x + 3y)dx + (9x – y)dy along the parabolic arc y = x? from (0,0) to (1,…

A:

Q: Evaluate the integral (2x +3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: x sin x Evaluate the integral dx using residues. (4 + zX)(I + zX)

A: Given ∫0∞xsinxx2+1x2+4dx=imaginary part of ∫cRfzdz Let, fz=zeizz2+2z2+4 Singularities of  fz where…

Q: 6) Find the length of the arc of the curve y² =x ³ from (1, 1) to (2, 2 v2) twice using two…

A:

Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: Find dy Ldx For the following (Jy)' =(In tan x)(x") ( sin x)"

A:

Q: Consider the integral (x) dx where f(x) is a smooth continuous curve. One or more of the following…

A:

Q: Find the length L of the arc formed by y = (-4x² + 2 In(x)) from x = 4 to x = 5 8 Set up: L = V1+…

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Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2…

A:

Q: QUESTION 6. Use an appropriate change of variable to evaluate the double integral: - x d A, cos y+ x…

A:

Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

A:

Q: Evaluate the iterated integral. x2 sin(y) dy dx

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

A: Solution of given question is written in below steps.

Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

A:

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x>12 from (0, 0) to (4, 32)

A: Solution is given below..

Q: Find the length L of the arc formed by y = (-0.5x2 + 16 In(x)) from x = 4 to x = 6 %3D •6 Set up: L…

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

Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

A:

Q: By using Beta function and assuming x2 = y, the integral %3D -1/2 dx is equal to

A: Substitute x1/2=y or x=y2:  ∫011-x1/2-1/2dx=∫011-y2/2-1/2dy2…

Q: Which integral expresses the arc length of y= In(cos x) from x = n / 6 to x = T |4? | sec(x) dx |…

A:

Q: Evaluate the integral (2x+3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A:

Q: Evaluate the iterated integral. /2 x sin(y) dy dx

A:

Q: Evaluate the integral | (2x + 9y)dx + (21x – y)dy along the parabolic arc y = x from (0,0) to (1,…

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Q: The value of (4xy- (sinx)³)dx + (x² + y9)dy (Correct to ONE decimal place) where C is the region…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. To evaluate the given…

Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

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Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: Determine the integrating factor Mlx,y) that will make the equahon (e* siny + 3y ) dx exact. Verify…

A: This is a problem of Exact differential equation. For equation to be exact, We will have to have,…

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1,1).…

A: Given

Q: Find the area under the curve y = sin 2t from t = 0 to t = π/4.

A: We have to find the area under the curve of a function y=sin2t , here we have the limit from 0 to…

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

A:

Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

A: