10-19 How much work is done in separating an electron (q = -1.6 × C) from an oxygen nucleus (Q = +1.3x 10-18 C) from a distance of 2.0 μm? Recall: (k = 8.99 x 109 Nm2/C2) F(r) = 1Q kQq r2

Q: Find the approximate value for |- 1 dx using -1 Vx? +1 (a) the trapezoidal rule, with h = 0.2, 0.1.…

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Q: 5 2. We know (using FTC) that Sº 3x² - 2x dx = 100. Use Maple to approximate this integral using the…

A: We approximate the integral using the Trapezoid Rule with Maple. With n= 32The solution using Maple…

Q: I need help on this q

A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: 4. What approach of integration by parts does solving ef cos(r) dr involve? a. separating b. cycling…

A: By part   ∫u v dx = u∫v dx −∫u' (∫v dx) dx u is the function u(x) v is the function v(x) u' is the…

Q: Using the substitution u = x³ – 1, ƒ±₁ x² (x³ — 1)5 dx is equal to which of the following? O O 63 -2…

A: Let, Put

Q: - 47 f(x)dx = 12 - 51 | and - 47 |. 9(2)da = 20 – 51 and - 47 - I h(x)dx = 32 - 51 what does the…

A: We can solve the integral as below.

Q: Exercise 1.2: Apply integration by parts a second time to get 272 2(1-2²) 2n x 2n 2(1-2²)-¹…

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Q: nto Usx) = S K(x5) K($st) f(t) dt d 3 %3D a Us CX) = Sfct)[ [K(x,3)K(3st)d3] dt %3D

A: Correction in equation 9: u2x=∫axKx, ξ∫azKξ, tftdtdξ     ………9 So, u2x=∫ξ=axKx, ξ[∫t=azKξ, tftdt]dξ…

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. у'3D…

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Q: 2.3 Next, integrate 22(cos(t))2n+1dt and show that it can be written as 2n I(n) = I(n - 1) 2n+1

A: Given integration .We have to show .

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: Calculate the order of the local truncation error of the Crank-Nicolson method for approximating the…

A: The heat equation given is as follows: ∂u∂t-∂2u∂x2=0 We are asked to find the order of the local…

Q: 5x -6 3x +2 5y

A: Any triangle with all its interior angles equal is called an equilateral triangle. Each interior…

Q: 3. Using integration by parts (IBP), what should you pick for u and du in 5z cos(3r) dr? = cos(3r),…

A: Integration By Parts formula is used for integrating the product of two functions. This method is…

Q: State ALL the theorems on integration used in the following computation: 2 2 (32- 3 d - 23 3 3 -0) –…

A: Remark: The sum rule of integration is  ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x.…

Q: 8.(5.4) Change the order of integration and evaluate. (1) I = √² S 1 1 cos(x + y) dy dx (2) I =…

A: Steps

Q: 00 Represent the function Σ as a power series f(x) = > (1 – 6x)2 Cnx" 73D0

A: C0=? C1=? C2=? C3=? C4=?  radius of convergence R=?

Q: Is this 2-form exact? w = x dx A dy

A: Given that ω=xdx∧dy To check this  2-form is  exact or not.

Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

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Q: Suppose one wants to use the Midpoint Rule with m = 2 and n = 3 to estimate the value for on the…

A: Given: Here is the given integral, ∬R5x2ydA midpoint rule with m=2 and n=3 Rectangle, R=0,2×0,1.5 To…

Q: dx. +44 43

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Q: Solve the following partial integral (a) J 3r444r -29 (b) J-4)2 ( 43) Using the Trapeziodal rule…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: (b) 8(r)g(t – r) dr

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Q: cosh (x – 3) dx 8 – cosh² (x – 3) 18. 12

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Q: 4) From the graph below 10 -20 -15 -10 10 15 20 -10 -15 a) Use integration to find the shaded area…

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Q: Calculate the derivative. f(x) = (x³ + 2) (x³ + x + 9)

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