Describe the domain of integration of the integral. хуdz dydx Choose the inequalities which describe the domain. O 0sx< 4, 0 < y < V16 – x², 0 < z< V16 – x² – y? O0

Q: Use method of integration by parts to soive the the integral :xs Xsen xd x

A: Given: I=∫xsinxdx for evaluating given integral, we use integral by parts theorem according to…

Q: Change the order of integration. 19 19 xe361 dydx The answer should be in the form ' f(x, y) dx dy,…

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Q: Evaluate using integration by parts or other techniques of integration. 2 9x √x² e ³x dx fx² e ³x dx…

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Q: Express the integral in terms of the variable u, but do not evaluate it. 7аr V 15 — 22 dx; и — 15 —…

A: Definite integration substitution

Q: 1 1 x) dx =x sin(2 x)-; sin(2 x) +x cos(2.x) + C x=(1+2x+2x*) e» +c (-2,x) (-2 x) (1+2 x+ 2.x²) e

A: The given integration is: ∫x2 cos2x dx=12x2 sin2x-14sin2x+12x cos2x+C To verify the Integration.

Q: Find the exact value of the integral using formulas from geometry. 10 V100 - x dx 2 10 |100 -x O 00…

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

Q: Q.2 Find area under the curve y = x² +1 over the interval [0,3], Using Riemann sum.

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Q: r = -1 r = 2 y = r 4 (2, 4) (-1,1) -3 -2 1 y = 6,

A: The given graph is:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Using double integrals, calculate the area of the region bounded by the lines y=x+4;   x=y+4;…

A: Given y=x+4,x=y+4,x=-y-4 and y=x+4

Q: An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

A: Topic - application of integration

Q: Use integration by parts to find the integral. (Use C for the constant of integration.)

A: Consider the provided integral,

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

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Q: Evaluate the double integral for the function f(x, y) and the given region R. (Give your answer…

A: this problem is related to integration and we solve this using double integration method.

Q: 3 dx (x2)Vx2+9 x²+9,

A: The given integral is: ∫3x2(x2+9)dx

Q: Evauate the definite integral. Use an appropriate substitution. Give the exal value as a fraction.…

A: To find : ∫12xx2+13dx Let u=x2+1. Then       dudx=2xdx=du2x ∫x(x2+1)3dx=∫xu32xdu…

Q: 19Eraluate the integral using Integration by parts, substitution,onboth it necessary. use Symbbolic…

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Q: Explain the terms integrand, limits of integration, yariable of integration, and describe when a…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: a) Evaluate the indefinite integrals using Repeated Integration by parts i) Sx²e-2*dx ii) Sx²Sinxdx

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

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

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Q: Using Integration by Parts, the integral [(x8. is equal to x10 5 - the above + 2x⁹) In x dx…

A: Given: I=∫x8+2x9lnxdx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: sin(x) dx =-x² cos(x)+2 cos(x)+ 2 x sin(x) + C e* s in(x) dx= 1 cos(x) + e* sin(x)+ C e*

A: Topic = Integration

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

A: ∫(2-x)2x dxApply linearity:=-∫(x-2)*2x dxIntegrate by parts ∫fg'=fg-∫f'gf=x-2 and g'=2xf'=1 and…

Q: Find the area between y=1.2x+2y=1.2x+2 and y=x2−4y=x2-4. Round your limits of integration and answer…

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Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

A: Indefinite Integration

Q: Express the integral in terms of the variable u, but do not evaluate it. 11x/10 – x2 dx; u = 10 – x²…

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Q: What are the limits of integration in the following definite integral? ∫05 5t2 dt  Select the…

A: To identigy the limits of integration in the given definite integral

Q: Change the order of integration. 16 4 Vx + 1 dx dy The answer should be in the form S f(x, y) dy dx,…

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Q: Express the integral in terms of the variable u, but do not evaluate it. | 7x /5 – x² dx; u = 5 – a²…

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Q: Solve using iterated integrals. (with graph) Find the area bounded by the circle x2 + y2 = 25, the…

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Q: 7- If you cant compute the value of integral exactly, you will use . 8- When f(x)-x'the value of…

A: As per guidelines, I can answer only one question.

Q: A cormpany manufactures mountain bikes. The research department produced the marginal cost function…

A: Evaluate the increase in cost

Q: Express the integral in terms of the variable u, but do not evaluate it. | 9x/25 – x² d.x; u = 25 –…

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Q: Evaluate the integral. Use integration by parts Sco-t x dx x cos'x+ V1 - x2 +C O x cos'x - 2V1 - x²…

A: Given query is to find the integral fo cos-1x.

Q: definiuon of the integral given in Theorem 4 to evaluate the integral. | (x +2x-5kdx Hint: > n(n+1)…

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Q: E Vatuate the given de finite Integral. Please write down the steps description. ース 2メ Type an…

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Q: y = x, y = 2x, x = 2

A: The curves y=x, y=2x, and x=2. We have to find the integration.

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: The trapezoidal rule states:…

Q: The Mean Value Theorem for Integrals guarantees the existence of a special point on the graph y = 2x…

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Q: Is it possible to evaluate the integral of a continuous function ƒ(x, y) over a rectangular region…

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Q: #2) The area of the region bounded by y = cos(3x), y = 0, x=0, T and x = is 12 The vertical line on…

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Q: In(xty) dA X-- (utv) 2 y-! (u-v) Kis the squave bounded (1,2), (2,3), (3,2), (2,1) by

A: The given integral is  ∫R∫ln(x+y)dA x=12(u+v)y=12(u-v) R is the square bounded by (1, 2), (2, 3),…

Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(4x)…

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Q: Match the Integrals on the left side with the appropriate tedhnique of integration to use on the…

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Q: In The value of the definite integral flm 12 √ex - 9 dx is in the form F(b) - F(a), where a JIn 9…

A: To evaluate: ∫ln⁡9ln⁡12 ex−9dx Let I =∫ln⁡9ln⁡12 ex−9dx Given: ∫ln⁡9ln⁡12 ex−9dx = c3-dπ Let ex−9=…

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 z√ 25z² - 49 √₂√² dz

A: Let's solve given integral.

Q: 6x3 + 5z? – 88z – 80 dr Consider the indefinite integral 16 Then the integrand decomposes into the…

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Q: an appropriate method. 1₁ Evaluate the integral using 1 x²√x² +9 dx

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