Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to π

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Evaluate the iterated integral: xy'e-" dx dy

A: Here we evaluate the iterated integral

Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: 1. Compute the following integrals. (a) dx. (b) 2° sin(x³) dx.

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Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

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Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: Use Romberg integration to compute R3,3 for the following integral x sin x dx

A: Given integral is, ∫01xsinx dx Then, h1=b-a=1-0=1h2=b-a2=12h3=b-a4=14

Q: what is the integral of e^(-2a|t|) from -w to w?

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Q: Evaluate the iterated integral. 74 (x² - 2y²) dx dy

A: Given that a double integral we solve this integration by using general property of integration.…

Q: Determine the following integrals: 1.1 G 3x³ +8 X dx 1.2 G 1.3 4x+6 dx x + 3x-10 sec² (sin 5x)cos 5x…

A: We have to find out solution

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Evaluate the derinite Integral. #5 In(x) dx

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Q: dx (1 – e²)² -1

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Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

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Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: Find a particular integral for y" + y' + y = 2 + x + cos x

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Q: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: Which of these is a non-elementary integral?" ( In(2y² + 1) -dy 4y A. * cosh(2x) xp. B. +…

A: (a) For, Is non elementary since y is in denominator. (b) For Is non elementary since x is in…

Q: 2. Find the indefinite integral (Scos(4x) + √x dx

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Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

Q: Calculate the iterated integral x² ,3 sin x dy dx.

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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: 1. Evaluate the integral r4-x² 8x cos Y dy dx Y – 4 by reversing the order of integration.

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Q: 1. Compute the following integrals. (a) dx. (b) x³ sin(æ³) dx.

A: We have to integrate both

Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: Evaluate the double integral of the function over the rectangle cos(2x) sin(y) dA, R = 0, 0, 2.

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: Evaluate the integral below. cos(y) dy dx /x/3 Select one: O a. sin 1 O b. O O c. 1 O d. sin 2 – 1 O…

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Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

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Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: Which of the following is not an improper integral? 1 dx cos x 2 cos x dx | cos x dx 0. 1 dx cos x 2…

A: Given, The definite integrals We have to find the integral which is not improper.

Q: 1 -) Prove the existence of the improper integral 1 (In x) sin – dx -

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Q: Evaluate the iterated integral. (x2 - 8y2) dx dy

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Q: Use Romberg integration to compute R3,3 for the following integral cos x dx

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Q: Evaluate the iterated integral. In 5 In 3 4x+2y dy dx e 0 1 In 5 In 3 | 4x+2y dy dx = 0 1 (Type an…

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Q: 1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

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Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

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

Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α<1 b)α>1

Q: Find a formula involving integrals for a particular solution of D.E y" + 3y" – y' – 3y = tan x

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