1. Given that f(x) dx 4, which of the following integrals can be computed using a substitution? If an integral can be computed using a substitution, evaluate the integral, detailing the substitution work. If an integral cannot be computed using a substitution, explain why a substitution would not work, in the absence of additional information. (a) xf(x²)dx (b) xf(x)dx (c) (x?)dx.

Q: Use a table of integrals to find the indefinite integral.

A: To find: The integration of ∫e3x1+ex3dx. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C…

Q: Evaluate the ff. integrals using substitution: dx 1. S (5-2x)2

A: 1. Using substitution u=5-2x

Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: Evaluate the integral, if it exists.    ∫0T (x4 - 8x  +7) dx

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Q: Evaluate the integral of (x^(3))*(e^(x^2))*dx

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Q: 1 use this fact and the properties of definite integrals to evaluate 3 (7 - 6х2) dx. Given that x²…

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Q: Take the integral from 0 to 2 of (x/x2+4x+8)dx

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Q: Evaluate the integrals.

A: To find the value of given definite integral.

Q: '1 1 Given that x² dx = use this fact and the properties of integrals to evaluate (8 — бх2) dx.

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Q: Evaluate the integrals ∫dx/4 + x2

A: Consider the following formula: ∫1x2+a2dx=1atan-1xa

Q: 1 use this fact and the properties of integrals to evaluate dx =3 (7 – 6x2) dx. Given that

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Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: Given the definite integral, its limits are to be substituted to x³ dx x + 1 x² x² 2 x3 3 Option 1 +…

A: Given problem:-

Q: c/4- 4 – x dx

A:

Q: b) Evaluate the integral In 5 (x + 1)²e* dx

A: Given integral is ∫0ln5x+12exdx

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: The given integral is ∫9x81-(ln x)2dx. The integration of 1a2-x2=sin-1xa+c, where c is constant.

Q: 2ea dx (ет — 1)2 1

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Q: [x² (-2 + x² )* dx

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Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: Evaluate the integrals ∫dx/2 + (x - 1)2

A: Evaluate: ∫dx2+x-12

Q: 4. Evaluate the definite integral by using substitution. x-1 dx (x+ 2)2/3 -1

A: given the definite integral is∫-16 x-1(x+2)23dx

Q: a.) ∫ (4x + 3)1/2  x-5/2 dx

A: Given:

Q: 1. Find the following integrals using the graph below: g(x) dx 24 g(x) 4 g(x) dx )dx g(x)dx

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x dx/√x - 2

A: Given Integral is., I=∫xx-2dx

Q: 1. Find the values of the following improper integrals with unbounded domains of integration, if…

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Q: 13. x-x dx x² +x?

A: We need to evaluate the integral ∫13x-x-3x2+x-2dx ................ (1)

Q: 7 For the integral 3xVx + 6dx, if we use the substitution u = x + 6, we can rewrite the integral in…

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Q: Evaluate the integrals

A: 1) ∫xndx=xn+1n+1+c2) ∫adx=ax+c

Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

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Q: 2. 21-/9 – 4ª dx

A: The by parts method is given as ∫uv=u∫v-∫u'(v) where u is the first function and v is the second…

Q: Evaluate the integrals.∫x2 cos x3 dx

A: We have  I=∫x2cosx3 dx                          ⋯⋯(1)   Let  x3=t3x2du=dtx2du=dt3 put in equation…

Q: Evaluate the integrals ∫ ln x/x2 dx

A: Evaluate the integral ∫lnxx2dx.

Q: Evaluate the integral analytically. 1 е бх 1+ e 6x

A: consider I= ∫01e6x1=e6xdx

Q: Find the indefinite integrals. S- 2x -) dx J(금 a)

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Q: Question 6 Evaluate the integral by using a substitution prior to integration by parts. In (9x +…

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Q: If g(1)=−5, g(5)=9, and ∫from 1 to 5 g(x)dx=−8, evaluate the integral ∫from 1 to 5 xg′(x)dx.

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Q: 6. Use the Method of Substitution to find the indefinite integrals: et*dt b) /; 9 xp=

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Q: + 3x dz. x2 + 1

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Q: Evaluate the integrals in ∫e1/x/x2 dx

A: Our Aim is to evaluate the integral given below:-I=∫e1/xx2dx -(i)

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: 6 Evaluate the improper integral, if exists : dx (5 – x)3 -00

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Q: 3 aluate the indefinite integral by using the substitution u = x + x° to reduce integral to standard…

A: Please refer to the image below

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: ,(x² – 4x)dx 1.

A: To solve the integration

Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

A:

Q: In x dx

A: To Solve for the integral