Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it to solve the dx integral f 2.

Q: A u substitution has been used to evaluate the following integral. [ ²₁ f(x) dx = [₁, 2²( [²₁x² (7 +…

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Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: The integral ₁₁x – y dxdy is equal to: Select one: 0 O2 O None of them -2

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Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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Q: Solve the following integral using substitution method: X S. dx √x²-1

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Q: Use the substitution formula to evaluate the integral. T/8 19) (1 + etan 2x) sec 2x dx

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Q: Evaluate the integral х3 dx x2 +49 х3 dх x2 +49 (Use C as the arbitrary constant.)

A: We substitute x^2+49=t, then the given integral become

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: Evaluate the integral below using 2 point Gauss-quadrature and compare your results with the exact…

A: Given that, the integral is ∫15∫065y3+2x2+5dx dy. Note that, the formula for 2-point…

Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

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Q: 4 x*dx J (x² + 1)²

A: Solution is given below:

Q: Find the indefinite integral. t2 dt 3= t3 +C

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Q: Evaluate the given definite integral using appropriate substitution: 8e2a dx @ 4e4 – 4 A © 4e4 + 4…

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Q: The integral 1 = [(x* + 5e* + vx )dx is equal to:

A: Given integral is∫x4 + 5ex +x dxevaluate....

Q: Use quadrature formula [f(x) dx = c f(0)+c₁ f(x) to approximate the value of the integral [x² In x…

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Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

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Q: Provide an appropriate response. Given fx) dx = 4 and g(x) dx = 2. use properties of definite…

A: We have to solve the integration

Q: Evaluate the definite integral.

A: Now consider,

Q: 7. S 8x³ e** dx il ww be 7dx 8. J sec x esinx bne

A: I am attaching image so that you understand each and every step.

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: Given:

Q: Use the substitution a 3 sin t to evaluate the integral f V9 – x² dx.

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Q: 2. Given the integral: e/x dx;n = 8 d) Use the Trapezoidal rule to approximate the integral using…

A: When n = 8, then h = 0.25 and given f(x) = e1/x

Q: To evaluate the integral dx, we substitute x = 2 sec 0. VAx-4 Select one: a. True b. None of these…

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Q: Evaluate the integral. (Use C for the constant of integration.) dx x² + 9 2+9 n(x+ Vx² + 9 ) +C ×

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: Evaluate the integral. NÓTE: Enter the exact answer. xy" dy dx

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Q: (b) Consider the integral I = So f(x)dx for the function 1 f(x) = -2e-* + 4 2x 120 Approximate I…

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Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: (b) Consider the integral I = f f (x)dx for the function f(x) = -2e + 4 1 x' +2x 120 Approximate I…

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Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: the integral , dx is equal to: -2 x2+4x+5 4 2 the above the above

A: We will find the solution of the integral.

Q: Find the integral 1 dx J x² + x + 4 +C

A: ∫1x2+x+4dx Consider, x2+x+4=x2+x+14+154=x2+2x12+122+154=x+122+154     ∵a+b2=a2+2ab+b2=x+122+1522

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: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Evaluate the integral F(= - 0)"dz, (x³ by making the appropriate substitution: u = P(* - 0)"de -…

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: Evaluate the integral. (Use C for the constant of integration.) R - 9x In(x) dx x² – 25

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Q: çin fxa-lex®dx dx 3?

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Q: (d) L™ x³ cos(x* + 5) dx. (e) f(2x – 1)³ dx . -

A: For the given integral  ∫0π4x3cos(x4+π2) dx

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: Evaluate the following integral. x2 dx V1- 144x x2 dx = V1-144x? (Type an exact answer. Use…

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Q: 1 dx. x+ v1+x

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Q: Q4: A) Evaluate the following integral using trigonometric substitution method: 3V3/2 x'

A: Integration is solved using substitution method.

Q: Evaluate the integrals dx Så (4-x²)²

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

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: Evaluate the definite integral. (a) S, (x³ – 6x² + e-*)dx (b) S G+ 2)dx

A: a) ∫02x3-6x2+e-xdx=x44-6x33+e-x-102 Formula: ∫xndx=xn+1n+1 and ∫emxdx=emxm=x44-2x3-1ex02…

Q: Evaluate the integral. (Use C for the constant of integration.) / G 6.9 + +0.5 +0.5 5ex dx 6 -

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.