Calculate the following integral by applying the transform u=(3x-y)/3, v=y/3 and integrating over a suitable region in the uv-plan

Q: Consider the definite integral. (8x – 1) e- dx Let u = 4x – x. Use the substitution method to…

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Q: Calculate the integral of f(æ, y) = 10x over the region D bounded above by y = x(2 – x) and below by…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Given:

Q: 6 (y/3)+1 (*) (3x-y dxdy 3 y/3

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Q: Compute the value of the following improper integral. If it is divergent, type D. 1 dx 0.

A: To compute the value of improper integral.

Q: Transform the integral fo o sin o sin 0 do de by the substitution x = sin o cos 0, y = sin ø sin 0…

A: Solution: The given integral is I=∫0π2∫0π2sinϕsinθdϕdθ The substitution is x=sinϕcosθ, and…

Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

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Q: Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

A: We need to find average value.

Q: Evaluate the integral dx (2x + 11) by making the appropriate substitution: u =

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Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: 6 0/3)+1 (3x-y |dxdy 3 y/3

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Q: Evaluate the integral by making an appropriate change of variables. I cos( 3 () a where R is the…

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Q: Compute the line integral of F(x, y) = (x3, 4x} along the path from A to B in Figure 19. To save…

A: Given :    F(x, y) = x3, 4x   To compute the line integral of F(x, y).

Q: evaluate the double integral xy cos y dA over the given region R = [-1,1] × [0, 7 ]

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Q: Evaluate the double integral (x +y)² sin(x – y) dA for R, which is square with the vertices (0, 1),…

A: Consider the given integral and construct a diagram based on the given conditions.

Q: Evaluate the integration: r sin(20)drd0 Over the area in the first quadrant bounded between two…

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) cos…

A: Put,  u=t differentiating with respect to t on both sides, dudt=ddtt12 dudt=12t dt=2t du  dt =2u du…

Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

A: where are is the trapezoidal region with vertices(8,0),(10,0),(0,10), and (0,8).

Q: F(x) = sin(t) dt %3D 3x

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Q: SSy'e»-'dy

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Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: 5. SKETCH the area D between the lines x = 0, y = 3 – 3x, and y = 3x – 3. Set up and integrate the…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

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Q: Use Romberg integration to compute Rg,3 for the following integral x sin x dx

A: Given integral is, ∫01xsinx dx Then we can write as, h1=b-a=1-0=1h2=b-a2=12h3=b-a4=14

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: dx%3D 9+x²

A: Solution is given below:

Q: Compute the line integral of the scalar function f(x,y) = sqrt(1 + 9xy) over the curve y = x^3 for…

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Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: Given

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Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

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Q: Compute the following double integral over the indicated rectangle (a) by integrating with respect…

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Q: Find the indefinite integral. [(sec e tan ()i + (tan t)3 + (2 sin t cos t)k] dt Integrate the given…

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Q: Write down the definition of the laplace transform in terms of an improper integral and use it to…

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Q: | 7x2 V2x3 - 1 dx

A: Here the given integration I=∫7x22x3-1dxNow Substitute as2x3-1 =u⇒6x2dx=duThus the integration…

Q: Use a double integral to find the area of the shaded region. 1/2 10 r= 5+5 cos e -5 5 10 -10

A: The integral of a function is with respect to two different variables, so if f is a function of two…

Q: Evaluate the double integral of the function over the rectangle cos(2x) sin(y) dA, R = 0, 0, 2.

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Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: Evaluate the integral. Clearly indicate u-substitution steps if required. 19 J2+ 5y

A: Given integral is ∫195+2ydy evaluating the integral with u substitution

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: 2) Find the total differential dz for z = tanhy In(x)

A: Total differential of z is given by dz=(∂z/∂x)dx+(∂z/∂y)dy

Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: Evaluate the integral S - dx V16-x2

A: Evaluate the integral of the integrand  x2/√(x2-16) .

Q: z · 3°dz

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Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: Evaluate the integral. (Use C for the constant of integration.) At dt te-4t

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Q: What is the Laplace transform of the convolution integral of h (t) = sinh 3t u (t), x (t) = cosh(3t)…

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Q: B.) SET up THE DEPINITE INTEGRAL OF THE SHADED REGION THAT WILL GIVE THE PARAMET ER AND AREA

A: Note:- sin2θ =2 sinθ cosθ Area = ∫r2 dθ Given that  C1 :  r=-3 sin2θC2 :  r= 3 sinθ

Q: Evaluate the improper integral if it exists dxp: 2.10 0.20 The improper integral diverges 30 2/2 40

A: Option (3) is correct. Integral diverges.

Q: Use a double integral to find the area of the shaded region. -3 -1 π/2 -3 r = 2 cos 20 3

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