For the field A = 5 cos(d) 3 , the integral along the path (2, T1/3, 5) to (2, T/2, 5 ) is equal to: %3D Cx13 O A. | 10 cos (4) dø = 10( -1) x/2 O B. None of the Given answers O C. zero O D. x/2 10 cos () do = 10(1– 21 R13

Q: Determine weather the statement is true of false. Explain your answer.

A: Consider the given differential equation dydx=1x2+1 Use separation of the variable method to find…

Q: The particular integral for (D2 + 12)y = cos20z is O yp (cos20z) 388 (cos20z) O Up 412 Yp = (cos20z)…

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Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: Which among the following is an improper integral? -0.5 dx a. O5- -0.5 1-x2 csc?x b. Si dx V5-csc2x…

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Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: T 4. Approximate the integral fo x cos xdx with n = 6 using the Composite Simp- son's rule.

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Q: Q5. Find the below integrals and √(2.20) 2717 dx(x) = 2₁ (0,00) 1 + X{0,3} + X(-3,-2)) "dX=? where A…

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

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Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

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Q: - 19 f(x+1)-(x2 - 6x +13) Ax + B √x²+bx+c² dx? (3)-In/x² - 6x + 13| + C The integral What is the…

A: Using partial fraction…

Q: By the even extension method applied to the function f (x) = e¬19x, where x > 0, the value of the…

A: Given, fx=e-19x where x&gt;0 using even expansion Let fevenx=e19x      -∞≤x&lt;0e-19x        0≤x≤∞…

Q: Q2/ Find the value of the following integrals: 1- |((x+ y)dx +(y-x)dy), when c is given by, x = cos…

A: We have to evaluate the integral is ∫cx+ydx+y−xdy. where c is given by x=cosθ, y=sinθ and 0≤θ≤2π.…

Q: Given dy – sin(x))dx + cos(x)dy, where C is the triangle with vertices (0, 0), (1/2, 0), and (t/2,…

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Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: Evaluate the integral. J-Txe* dx -7(x +1)e -*+C a. O b. -7(x – 1)e*+C Oc. 7(x +1)e-*+C O d. 7xe-* +C…

A:

Q: 15x? – x3 – 43x – 19 - - The integral | can be rewritten as (x + 1)²(x² – 6x + 13) Ах + B + lax² +…

A: Given: The given integral is ∫15x2-x3-43x-19x+12x2-6x+13

Q: x" e ax n-1 ax dx e ax dx Use one of the reduction formulas shown to the right (which are valid for…

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Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

Q: dx e2a +5

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Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: Q1) A-Evaluate the following integrals: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x-2.…

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Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx =…

Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

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Q: ( a ..    )Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2…

A: Given, ∫01cos2x dx

Q: Suppose F(æ) = | sin(t +t – 1)dt, and F(x) G(x) = 3x2 +4 DO NOT attempt to evaluate the integral -…

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Q: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

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Q: Which of the following is an improper integral? dx 2 2r+8 B -4 x2-x-2 -1 xe Cos (x)dx -2

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Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

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: 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: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: A uniform electric field of magnitude 400 N/C is directed parallel to and in the direction of the…

A: Given: Electric field of magnitude = 400 N/C Now, Electric field equals to the gradient:

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: What is the integral of x" cos ax dx ? хN sin ax А. -=S nx"-1 sin ax dx + а а хN sin ax B. n -"Sxn-1…

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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: -Jxcar (r<)= o x sin(ñ x) cos (Tx)

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Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

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Q: n/4 3x Approximate the integral e "sin(2x)dx using both Simpson's rules with n = п/12

A: Given: I=∫0π4e3xsin2xdxn=π12

Q: Select from the subsections, the one that corresponds to a step of the solution procedure of the…

A:

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: 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: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: Evaluate the integral V16 – x2 O A.8 sin-1(프) - 특V16-22 +c O B. sin-1(플) + c O C.8sin-1(플) - n. V16-…

A: Option (a) is correct.

Q: 1. Evaluate the following integrals. 3r5 (a) / dr V2 – x3 2" + e2" sin(2") sin(2=) dx 2x +3 (c) / dx…

A:

Q: Find the integral of (1 + 2x)e^(-x) dx from x-0 to x--. A. 3 B. 4 C. 2 D. 1 O A B. DI

A: Use integration by parts for solving it,

Q: Q2/ Find the value of the following integrals: 1- [(* |(x+ y)dx + (y - x)dy), when c is given by, x…

A: The line integral ∫CF1dx+F2dy involves the integration over a specific path. In this problem, we…