p) By using integration parts, show that i. S(In x)²dx = x(In x)² – 2x In x + 2x + C.

Q: Evaluate the double integral. |/ (2x + y) dA, D = {(x, y) | 1 < y< 4, y – 3 < x :

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Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

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Q: .2 (3 – z)(3z + 1) dz

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Q: 26 1 dt. (b) Use the integration capabilities to evaluate the integral

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Q: Solve for the areas of each color using Definite Integration. A (,V 25-x² dx) – (L, V16 – x² de) =…

A: Given:

Q: To integrate y3xdx we apply integration by parts and in the form u dv, u is set as:

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

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Q: 1DEvalvate the integal usiing Integration by parts. J5 sin ? Cx) dx -ユ Express numbers in exact…

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Q: By using integration parts, show that . [In x)²dx = x(ln x)² – 2x In x + 2x + C

A: We are asked to find the integral.

Q: 4-x? Change the order of integration | | f(x, y, z)dzdydx in the order dydxdz.

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Q: dz 4z+z' ,2

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Q: Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by…

A: greens theorem

Q: Q5A) Find volume of body from above Z = √√4x² - y² and below Z - Triple integration. 1 using

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Q: 3. Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along…

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Q: c) Evaluate | V In(z)dr by using integration by part.

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Q: 8. What domain D in space minimizes the value of the integral // (4x² + y^ + z2² – 4)dV

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Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

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Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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Q: .2 What is the reversed order of integration of 1 dxdy? a. II Vx* +1 dydx 0, O b. x4 +1 dydx 0, .8…

A: Topic:- application of integration

Q: Use the property to estimate the best possible bounds of the integral. II. 5 sin“(x + y) dA, T is…

A: To estimate the best bounds of the integral.

Q: (b)

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Q: Solve fx² In(x) dæ using Integration by Parts. Use u = In(x) and v = x?. Answer:

A: Topic = Integration

Q: 02:- By using integration by part, find :- (Choose two only) 2-f Inx (x') dx

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Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

A: off

Q: r' y +3y+1 dy y" + y´ +1 2.

A: As per our guidelines, we can answer only one question. Please repost the second question again. The…

Q: Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine…

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Q: * Using integration by parts, the integral sec dx is equal to @ secx +nlsecx + tanx| + C 1 1 secx+ A…

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

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Q: Use 73 rule with four segment, and i) Simpson's 3s rule ii) Simpson's to obtain the integration of:…

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

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, u is set as: Ox

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Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: By making an appropriate change of variables, evaluate the double integral -y², I = || ( + y)e* v°…

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Q: Using the integration bay parts formula with u = x- dv = cos x dx, the integral x cos x dx becomes

A: The given integral can be solved as follows:

Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: 3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1…

A: Integral by parts

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: 6: Change the order of integration; -1 f(r, y)dydr + f(r, y)dydx

A: Interchange the x and y limits For first part y=x⇒x=y2x=0, y=0x=1, y=1∫01∫0x f(x,y)dydx=∫01∫0y2…

Q: Calculate the double integral. 8x dA, R = [0, 8] × [0, 1] 1 + xy

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Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: 2 Sphere S to be the top half of sphere · x² + y² + 2² SS₁zdS /5 calculate the integral.

A: The given Surface is the top half of the surface x2+y2+z2=a2. To Evaluate: ∬zdS.

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: use integration by parts to establish the reductionformula.

A: To prove, ∫xnx+1dx=2xn2n+3x+132-2n2n+3∫xn-1x+1dx

Q: Use the property to estimate the best possible bounds of the integral. II 4 sin*(x + y) dA, Tis the…

A: Consider the given integral: ∫∫T4sin4x+ydA T is a triangle enclosed by lines y =0, y = 2x and x =3.…

Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

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Q: Find the limits of integration with respect to u and v

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Q: evaluate using Integration by Parts.

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Q: 3. Use integration by parts to evaluate (x²+x+1) sin(r) dr.

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Q: - 1x Xe de

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Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

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