19 When approximating / f(x) dx with 10 rectangles, what is Ax? 1.8 18 O 19 10 1.9

Q: Find the smallest integer n to guarantee that the error in using Tn to approximate | e dx is e less…

A: The integral is ∫01ex2dx  The error of Tn is obtained by the formula is E=-b-a212n2f''c We want…

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 4 Given the integral: Jo 1+x² dx. Evaluate using Romberg's method. Tolerance = Nx10-6

A: Given integral, I=∫014 1+x2dx To find: Value of integral using Romberg's method

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: 5. Integrate the following by first using the rule (elnx = x) to rewrite the exponential part and…

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 43. (In z)² dx

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Q: 1) Use Simpson's Rule with n=4 to calculate S x² dx.

A:

Q: 17. Why doesn't the definite integral 1-x² dx make sense? (Hint: Think about domains.)

A: To find: The reason why the definite integral ∫231-x2dx does not make sense. Explanation: Substitute…

Q: Use the error bound to find the smallest value of N for which Error(SN) < 10-º. 6er dx (Give your…

A: Given  ∫016ex2dx

Q: The integral S.¹0 d 10 x²+6 x-8 is improper. dx

A: The given integral is (x2+6)/(x-8) , limit from 6 to 10.

Q: Jse the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) 1, dx, 1+x2 I =

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Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

Q: 35 If fis continuous and the nearest integer f(x) dx 126 , find f(7x) dx . Please round the answer…

A: We have

Q: ·In(x) 8. dx

A:

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: In(3) e Ver +1 dx In(2)

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

A: let f(x)=17ex2 differentiating four times to get fiv(x) because the fourth derivative will be non…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 | (- 2* + 20z – 96z?…

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Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: 6. Use symmetry to evaluate the following integral. (6x* - 5) dx

A: Given: -

Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

A: The composite Simpson's rule approach is a frequent way to deal with issue. To accomplish this,…

Q: The approximation of 3x e sin(2x) dx by Simpson's Rule is 2.584696

A: We have, ∫0π4e3xsin2xdx Let Number of subintervals be 30.…

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

A: We need to find how large should n be.

Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x³ – 3x2 + 2).dx

A: Formula Used: Simpson's 1/3 Rule ∫y dx=h3(y0+yn)+2(y2+y4+ . . . )+4(y1+y3+y5+ . . . )

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: The integral that represents the length of the .3/5 curve y = x5, where 1 < x < 3, is the following:…

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Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

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Q: /3+ |æ| dx -3

A: Given integral, ∫-333+xdx

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

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Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: 7. Evaluate the following integral or state that it diverges: Lo xe* dx

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Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

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Q: If df between= 3, and df within=60, if alpha is set at 0.5, then f crit =

A: Given:Degrees of freedom between = df1 = 3Degrees of freedom within = df2 = 60Level of significance…

Q: 169 dx Evaluate the integral x( In x)° 13

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Q: Q/ Find an integating factor for the diff- equ. 2y dx + (3y-2x)dy20? to

A: Conversion of non exact differential equation  to Exact differential equation. Given differential…

Q: 7. Evaluate the integral x4 6x5 1 dx

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Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: —3г — 7 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

A: