Find the exact value of the integral. Question 1 4 V2 + x'dx dy

Q: 5). S 13+1)E dx (Improper Integral)

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Q: Question 20 Which of the following is an improper integral? In(x4+1) dx -1 In3e COSX dx xe dx -4…

A: solution

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: Find the complete integral of the equation (p² +g°)x= pz dz dz where p=- q == ду dx

A: Consider the given partial differential equation as p2+q2x=pz, where p=∂zdx,q=∂zdy Rewrite the…

Q: S (3 – x)°x*dx

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Q: Question 17 Which of the following is NOT an improper integral? x-dx A -2 Vx2-1 x/2 sec x dx 01 x13…

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Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: Q3/ Choose the correct answer to evaluate the following integral 1 dx I = 1 (1 – x+)Ź

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Q: 5. 5 S x ³e x² dx

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Q: Question#4: Evaluate the following integral using the Trapezoidal and Simpson's rules with n = 10 In…

A: We can find numerical integration by using of following two rules: Trapezoidal Rule:…

Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

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Q: Question 1. Evaluate the following integrals using substitution method: |(x-1)(x²–2x)"dx_ a) sin°…

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Q: GIVEN dx x² +2x +2 Find the value of the improper integral if it exists. SOLUTION TO QUESTION 10…

A: To evaluate the integral: ∫0∞dxx2+2x+2 Solution: Evaluating the given integral.…

Q: a In x dx for the integral to be equal to 2 What should a be in O e? 0. 1 o 1 Ое

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Q: Q4: Solve the following integrals:- dx 4dx (1) S: (2) S: sec xesin x (3) S x sec? x dx 2+cos x

A: Note:-  As per our guidelines, we can answer the first three sub-parts of this problem. For the…

Q: Q4: Solve the following integrals:- dx 4dx (1) f 2+cos x (2) J sec xesin x (3) Sx sec? x dx dx (4) )…

A: Indefinite Integration

Q: solve the following Guassian integral : (yi – Y;) – (0; – 0;)e V21

A: Given integral is, Now,

Q: Question 4 Evaluate the following integrals: (a) / dæ x2 +4 * T/4 (b) etan(x) sec? (x) dæ 0. x3 – x2…

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Q: Find Particular integral (D' +1)y =e

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Q: Find the integral |(2 + 1)e* dz. (z + 1)e²² dz +C

A: solution is given below integration by parts...

Q: 2л I7 ở sin(4)dp do dp 0.

A: To evaluate: ∫0π∫02π∫05p2sinϕdp dθ dϕ Evaluating the given integral, ∫0π∫02π∫05p2sinϕdp dθ…

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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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: Question 3. Compute the following integrals. 3.1. S(4x2 – 1)'x dx - 3.2. Sx e5x dx 3.3. S x?cos xdx

A: 31) The given question is =∫(4x4-1)4xdx now first of all simplify the function. (4x4-1)4=(4x2-1)22…

Q: Question 2 Estimate the integral I sin (x) dx by the trapezoidal rule using n = 4. а) О0.7000 b) O…

A: Option C is correct.

Q: I. Solve the following integrals using Algebraic Substitution 1. ſ 2. S -1dx dy y+4-2

A: ∫un du = un+1n+1+C ∫1au+b du =1alnau+b+C ∫1u2+1du = tan-1u+C

Q: By making the change of variables t = x? in the integral that defines the gamma function, show that…

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Q: 1. S √x dx VX +1

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Q: Question 5. Evaluate the definite integrals. a) 8x dx .5 b) S 2 dy

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Q: Question 5 Estimate the integral sin* () dx by Simpson's rule using n = 4. a) О0.12082 b) 0.06041 O…

A: Apply Simpsons rule…

Q: 1- xy dy = 0. 1+ xy

A: 1+xyx2y.dx+1-xyxy2.dy=0 (Now multiply both sides by (x2y2) ): y1+xy.dx+x1-xy.dy=0 or,…

Q: Question 2 Evaluate the following integrals using the appropriate rules of integration. 2.1 S(cos x…

A: (2.1) Given- ∫-π2π2cos x-1 dx To find- Evaluating the above integral using appropiate rules of…

Q: Question 6 Estimate the integral 1 dx by Simpson's rule using n = 8. Vx3 + 4 a) 00.9361 b) O1.0212…

A: given integral :

Q: The value of the improper integral, if exists: S. 12 x e-a dx 1

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Q: Question 12 > x8 dx (29 + 7)? The integral is divergent.

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Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: 1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

A: (a) Given: ∫0πt sin 3t dt Apply integration By part : ∫I.II dx=I∫II dx-∫ddxI∫II dxdx Take: I=t and…

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

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Q: QUESTION 12 Evaluate the integral by changing the order of integration in an appropriate way. x sin…

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Q: Question 1 (i) Determine the following integrals (a) |cos? xsin xdx 1 -dx (b) J -5x+6 x² – (c)…

A: We have to find the integrals.

Q: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

A: Explanation of the solution is given below...

Q: If V (t) is the amount of oil in a barrel being filled at time t, what physical quantity is…

A: Let's find.

Q: Evaluate the integral , xy dx dy 0.

A: Here we will integrate function w.r.t. x first then w.r.t. y

Q: Question 16 Which of the following is one of the correct/convenient steps to evaluate -+dx which…

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Q: 3. Find the following integrals. dx S- a. +a?

A: Explanation of the solution is given below...

Q: Question 1 For each improper integral below, show that it diverges or find its value. (a) / Valnz…

A: Solve the improper integrals, a) ∫07x lnxdxb) ∫04lnxxdx

Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

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