2x For x > 0, In (t +1) dt %3D da A In (2 +1) In (8z + 1) 2 In (2 + 1) 3. 2 In (8z +1) E 24x In (8z + 1)

Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

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Q: Reverse the order of integration in S S(2xy + 1)dxdy and then evaluate.

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Q: 3. Integration by parts a.j 18x ( x+ 4)»

A: Given

Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A: The integration are

Q: 3. Reverse the order of integration in S(2xy + 1)dxdy and then evaluate.

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Q: d Q. * VE In(t)dt equals dx a. 4x³ (ln x) – 2 In(2) b. 4x³ (In x) – v2 ln(2) c.4x° (In x) d. 16x°…

A: Using leibniz integral rule -…

Q: Evaluate the integral. 2+e-2x dx e3x 10 +C O -2e-5x(5e3x + 1) + C e Sx(10e2x + 3) + c 15 1 e 3* 2e2x…

A: The given integral is ∫2+e-2xe3xdx. Evaluate as follows.…

Q: Show that the value of Vx + 8 dx lies between 2V2 - 2.8 and 3.

A: According to the question, we have to prove that the value of integral ∫01x+8 dx lies between 2.8…

Q: 7. Evaluate the integral: - dx 15x – x А. c. -2*+C +C с. 2.x 5+X +C 5+x +C D. В.

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Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

Q: Find an integrating factor to the linear D. E. In(9 x+16)y+ y =20 9x +16 p(x)= (6 x+ 14) In(18 x…

A: Given the linear D.Eln (9x+16)y'+99x+16y=20we need ti find the integrating factor

Q: Integrates PDE SE ニー Zく Z8 te

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Q: 1. Evaluate S(x + y)dxdy by reversing the order of integration.

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Q: Which of the ff is equivalent to the double integral: a. f¹ ln(2x) − In(x + 3) dx b. ln(x + y) -…

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Q: Q3: Reduce the integral Sx³J2(x) dx to integration in terms of Jo(x)

A: To find - Reduce the integral ∫x3J2x dx to integration in terms of J0x.       Formula used - Bessel…

Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

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Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: 1. Perform the antidifferentiation. (a) S Vã (7 –) dx (7 pts)

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Q: Evaluate the Integral dx 4. S V1-e-2x

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: Evaluate the integral: 1. - 1 (1- 5x + x³ – 2x5 5х + x3 — 2x5 dx x2 2. S(y³ – 3,/y+ Vy) dy

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Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: 2. Evaluate the integral. -2 (a) (x² – 3x) dx - -1 •3 (b) Lce L(e + 2)(t – 3) dt -2 (c) 2.9 x° dx

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Q: Evaluate the integral Зx2 — 4х — 9 A В + C dx using x3 – 2x2 – 9x + 18 - 2 x +3 – 3* х — х — 3x2 –…

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Q: 3 a) Change the order of integration and evaluate: | | dr dy 0 0

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Q: Find the integration of (1+ 2x)dx using Trapezoidal and Simpson's Rules for n=6

A: Given integral  ∫061+2xdx The Trapezoidal rule states that…

Q: Which of the following can be evaluated directly by the Power Formula of Integration? Sx³ V25 – x4…

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Q: In x)2 To evaluate aX, apply integration by parts twice. For the second application of integration…

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Q: 2. Reverse the order of integration and then evaluate. So S, x² sin(xy)dxdy а.

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Q: The integrating factor of the given DE are already given below. What is the value of “n” y2dx…

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Q: Find the Integration of: Ja (3sint + esin t) cost dt In 3 2

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Q: Q2: Find the double integration ff (4x + 2)dydx D={(x,y):0<x<2,xẻ<y<2x}

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Q: Evaluate the integral: dx 4 4V x -4 + =(x²-4)/2 + c 8 x - 4 + 3/2 + C ******** 3/2 (x²-4)2 + C -4+C

A: We have to evaluate the integral value.

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: How do I find the definite integral of these problems?

A: (a)

Q: 2. S*3*+2 dx x+2

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Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…

Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: 2. Integrate: x² In x dx a. Inx+c b. [(In x)² ++ c c.[(Inx)² - Inx++c d. none of these

A: To evaluate: ∫x2ln x dx

Q: Evaluate using integration by parts o D (x²-3) e² dx е

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Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

Q: Q1\ Evaluate the integrals: 10 A. S- V16+x2 В. Г(3 — 2х)-5 dx

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Q: A Evaluate the following integrals. 1. S2 dx 2. S6x dx 3. f9° dt 4. S-15x dx 5. S(3x - 4) dx 6. S(7u…

A: As per guidelines, I can answer maximum three subparts of a question. Since you have asked for 11…

Q: 2. Integral A e3A dA

A: