59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where a,b are constants such that a # b.

Q: 1. Evaluate the following integral: la 2x³ 2x5-x-4x³ + 1 (a) analytically, (b) single application of…

A: NOTE: As per the guidelines we are supposed to answer only 3 subparts question. Please upload it…

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given:

Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

Q: 1. Find the following indefinite integrals (any 4) +3x ii) [(2{/x* - 7x' +10e* – 1)dx iii) [(x²…

A: To evaluate the given indefinite integral.

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: 1) Find dy/dt for if : y = log2 (81n 2) 2) Evaluate the following integral= In 2 log2 (x + 2) dx x +…

A: Any logarithmic function having a base other than e can b converted to a natural log as shown below:…

Q: Give the general solution to x²y" + xy' + (4x² – 9)y = 0 in terms of Bessel functions. |

A: We need to find solution in Bessel function.

Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…

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Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: Evaluate the double integral: ∬ 4y/(1+x2)dydx y runs from 1/2 to 2 x runs from 0 to 1

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Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: [2.73 Find a general Solution of following monhomogeneous limear 1ogeneous linear ODE g+ +1+#)は = e…

A: non-homogeneous differential equations

Q: 8 4 8 Suppose that f(x) dx = 7 and f(x) dx = -6, and g(x) dx = -1 and g(x) dx = 4. Compute the given…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 3. Suppose o1 and o2 are solution to y" + ay +by = f, where a and b are real constants and f is a…

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Q: 21.14 Evaluate the following double integral: (x² – 3y² + xy') dx dy -2 Jo

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: x 3*dx Jo

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Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: The following integral is  The integral of g(x)dx from 7 to 2

A: The given integrals are,

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

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

A: We can solve this as follows:

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

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Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: d ** If g(x) = [e² – In(2t + 1)]at , find g" (x) dx A ex- In(2x + 1) 4 ex - (2x + 1)2 B (c) none of…

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Q: 2. Evaluate the given integral. S1– x if æ > 1 | 2² – 1 if a <1 f(x) dx, where f(x)

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Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: 57 Evaluate the integral |[xy dy dx. 12

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: z'e? dz

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Q: 1. Find the following indefinite integrals (any 4) (2/x* - 7x' +10e* – 1)dx (x* + 1)e* iii) dt +3x…

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: ** If g(x) = S [e* - In(2t + 1)]at , find g"(x) dx ex. (2x + 1)2 A ex – In(2x + 1) 4 ex + (2x + 1)2…

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Q: (4z + 5)² tan zy= + dr Cos z

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Q: メ1+ x€ Lat F Cx, x = F•dr whera yer CIS elosed c is Sagmants from C0,3) to Co,0) than from C3,0) to…

A: Given F=yexyi +xexyjand path is closed

Q: (2) Compute the following integrals. *T/4 (a) ) sin (4r) cos (4xr) dar. (b) / cos(kx)e l dx, Hint:…

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Show that +2100 kT te kT = [0 – 0] = 0; t from 0 to o

A: We need to show thatkTte-t2KT0∞=[0-0]=0where t from 0 to infinity

Q: Solve the following nonhomogenous PDE ‚²u + sin(3rx), du 00 and the initial conditions u(x, 0) =…

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Q: 3. Express the general solution in terms of Bessel functions: z²y" + 4ry' + (x² + 2)y = 0

A: Thanks for the question :)And your upvote will be really appreciable ;)