Problem 2. (a) Interpret | V1- (x – 1)² dx as an area and calculate the integral without integrat- ing. (b) Interpret x² + y? dydx as a volume and calculate the integral without -VI-r integrating.

Q: QUESTION 2 a) Evaluate the following integrals with respect to x. i) f9x cosech (3x)dx -0.5 xsin¯'x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: fcot(x) dx

A: First written cot(x) into cosine and sine form and then by substitution find the integral.

Q: the value of the integral dx 4.x(ln(9x))² 2

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: HiW 4i Solve the Pollowing Integral dy y-zy-3 16x3 dx 4火 -4X +1

A: According to our guideline we can answer only one question and rest can be reposted.

Q: QUESTION 2 Integrate the following integrals. a) S(3x² – 6x +4)dx b) 2cos 2x++ Vr - |dx

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Q: 1 2y³ .2 бу? dy y²

A: Given: ∫212y3-6y2y2dy

Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: PROBLEM 5.2: R is the region bounded by the following graphs: A1:y = /25 – x² x2 A2:y = - - 2 A3: y…

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Q: If - 1 | f(2)dr = | f(x)dæ + / f(=)dr - /. f(æ)dx, what are the bounds of integration for the first…

A: I have used the properties of integration

Q: Q8 Integrate by parts: x sin x dx

A: .

Q: Problem 1 Use integration by parts to evaluate the integral.  ∫5x sin(x)dx= _____________ +C

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Q: Problem 9  Evaluate the definite integral  ∫ ((10x^2)+7)/( sqrt(x)) dx Upper limit of integration=5…

A: The given integral is

Q: Problem 4. Evaluate the double integral by first reversing the order of integration. LL cos (2*) dz…

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Q: 10 | (2)dr = f(x)d.r + / f(z)dz f(x)dz, 2 what are the bounds of integration for the first integral?

A: Given,           ∫abfxdx=∫-28fxdx+∫810fxdx-∫-25fxdx

Q: Problem. 11 : Evaluate the integral by reversing the order of integration. 5 5 2e"/y dy dx = ?

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Q: Problem 2 Reverse the order of integration and evaluate the integral. 1. ó Sen dy da

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Q: Question 3 Calculate the following integrals: (6х-5)dx 3.1 I = S V3x²-5x+6 dx 3.2 I = S; 1+vx+1

A: Topic:- indefinite integration

Q: zr² sin 0 dz dr de Jo Jo EIN

A: Triple triangle is defined as volume. Using the integration of power rule and integration of Sine…

Q: Problem 7 Use integration by parts to evaluate the integral.  ∫ (upper limit=7, lower limit=1)…

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Q: y Problem 4: Find the centroid of the shaded area between the curves by integration. Y1 = cosx Y2 =…

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Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: What is the particular integral of the equation (D 2+9) y= x Cosx?

A: Use basic properties and formula, get PI of given equation.

Q: Problem 2. Compute the following integrals using integration by parts. Show your whole set-up not…

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Q: Problem 8  Evaluate the definite integral  ∫ ((12x^2)-2x+2)dx Upper limit of integration= 7 Lower…

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Q: QUESTION 1 Find (1+2x) In5x² 2x) In 5x² dx by using integration by parts.

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Q: Problem 3. Determine whether the improper integrals converge or diverge a) sin(x²)dx b) cos(r²)dx c)…

A: Check whether the improper integral converge or diverge.a∫0∞sinx2dxb∫0∞cosx2dxc∫0∞sinxsinx2dx

Q: dy dx=? 3.

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Q: Problem 1. Solve these integrals using substitution (a) x(x-2)³ dx, (b) text² di dt.

A: The given integrals:a∫xx-25dxb∫te3t2dtWe will solve them using substitution.

Q: +1 dx xe -3

A:

Q: Problem 22  Evaluate the indefinte integral.  ∫dx/((16+x^2)^2)=______________________ +C

A: First we assume Then we integrate by substitution

Q: (2 |2* 2 –1 – 1|x dx

A: Topic:- Definite Integration

Q: Problem #6: Evaluate the following integral by reversing the order of integration. 4900 10 Vr +4 dx…

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Q: Problem 3 Evaluate the following integral using integration by parts (and show your work): Sa³…

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Q: Problem 2 Use integration by parts to evaluate the following integral.…

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Q: Problem 20  Evaluate the definite integral:  ∫ |x-4x^2|dx=  Upper limit of integration=5 Lower limit…

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Q: Problem 11 The volume of the solid obtained by rotating the region enclosed by  y=(x^2), y=6x,…

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Q: - dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: QUESTION 3 3 Given the double integral, e dxdy. 0 3y

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Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: Question 2 Evaluate the following integrals using the appropriate rules of integration. r9 b-Vb db…

A: Consider the provided integral, ∫49b-bb3db Evaluate the provided integral. We can write as,…

Q: Problem 10  Use integration by parts to evaluate the indefinite integral.…

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Q: Problem #4: Evaluate the following integrals by interpreting them in terms of areas. (a) 11 |x - 8|…

A: Problem-4 (a)

Q: Problem 10  The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=2x, about…

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Q: Problem : 2 2y+z dy dI Evaluate the double integral :

A: ∫05∫0x2e2y+xdydx

Q: Work Problem 1 Evaluate the integral 13 (x+3)°dx

A: Topic = Integration

Q: Problem 2 Evaluate the integrals. (a) •1//2 4 dx 1/2 (b) V3/4 dx 1+16x2 (c) | tanh (x) dx (d)

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Q: Question 14 If we let 4=V5+x, the integral -1 is equivalent to V5+x

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Q: Question 1 Employ integration by parts to compute dx = ax'e- + de + K.

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Q: PROBLEM [ B3 ]: Evaluate the double integral: 6. dy dr

A: Consider the given integral. ∫04∫x2x46ydydx Start with the integration from inside. Use the formula…

Q: l Evatuate integrals t- 6 dx 4-25x

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