Let 1-ff Sysin(r' dvdy . By reversing the order of integration of 1,

Q: Evaluate the integral ∫1/ √tcos (√t+3)dt

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Q: Evaluate the iterated integral: dydx. /4 Jx²

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

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Q: Show that the following line integral is path independer (3,5) y² %3D cosh( )(10xdx +6ydy) (0,0) 3

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Q: Evaluate the integral. 4 (5 - t)Vt dt

A: The objective of the question is evaluate the definite integral.

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4- 3.…

A: Given:

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

A: Given : Functions f(x) = 2x and g(x) = 0   To find : Net area of f(x) and g(x) from [-3,3]?

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: Сompute 1. f dx, where f(x)=|x|.

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Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: By using the substitution method, show that for any positive numbers x and y ry 1 dt = Sdt

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: By sketching the graph aud using Integration, Find the ared of the regim bounded by tue paraboka…

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Q: Evaluate the double integral S ry° dydx

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

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

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: Evaluate the integral: ∫ t2 sec2(9t3 + 1) dt

A: The given integral is, ∫t2 sec29t3+1 dt. Apply the u-substitution by taking u=t3. Then dudt=3t2.…

Q: Evaluate the double integral.18. , D is bounded by y = x, y = x3, x ≥ 0

A: To evaluate the double integral. Given that  D is bounded by y = x, y = x3, x ≥ 0. We can define…

Q: Evaluate the iterated integral: dydx - 1/4 Jx2

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Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

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Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: Lex+3y dxdy

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Q: find the product of the integral 1- Sn) xy evx² dydx

A: To evaluate the double integral, first find the integral ∫0ln7yex2ydy. Consider the substitution…

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Use the Trapezoidal Rule to evaluate the integral fx-¹dx. 1 2|3 NIC 34 2

A: We have to evaluate the integral ∫12x−1dx by using the trapezoidal rule. Here, a=1 and b=2 And…

Q: What should be the rewrite of the integrand of dx so that the resulting integral is integrable?.…

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: compute J secx dr. I n trying to integrate

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Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: Use two -point gaussian square to approximate the following double integral:

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Basic:-(1) Differentiation : dxy = xdy + ydx.(2) Integration of :- ∫ dx = x + c(3) ∫ xn dx = xn+1n+1…

Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: e that ZIval = iatbisla,bez3 is an integral doncain

A: We have to prove given result:

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

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Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: Compute the line integral of F = (-y, x) along the line segment from (0,0) to (1,1).

A: The line integral is evaluated using the following formula  ∫cF→x,yds=∫abF→rtr'tdt    , a≤t≤b   ,…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=3,…

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Q: Evaluate the integral AP R = [0, 2] x [2, 4] × [-1, 1]. (y + z)2

A: As per the instruction, we will be solving only the first one.…

Q: Integrate: dr z2 + 4z + 8

A: We will integrate the above expression.

Q: Evaluate the iterated double integral. I 3 3y be dady A

A: