6. Evaluate: cin 4 a) (4x – 3) dx c) S* 2e* dx b) L, x²(-2x³ – 3)* dx d) ƒ dx e) S,(x + 1)(x² + 2x + 3)* dx

Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: 1 Prove that 3 dx s VI VI

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: Find 1-a Conf int for y txo P( - tor;ou L T L tarziv) =1-a

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Q: 5 (show resulting de) 2xdx - dy=x(xdy - 2ydx) When: x= -3 , y = 1 %3D

A: Differential equation and it's solution

Q: Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A: Given:        ∫02x2+1dx       n=4 , a=0, b=2   Midpoint Rule…

Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: 4 5y²-8X+6) dx =?

A: To evaluate the given definite integral

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

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: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

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Q: Queston 3.1.1. use the 2xc to approximete dx. Composite Trapezoidal rule with n=4 integral. 3.1.2.…

A: Let us consider y=2xx2-4. We have to compute the approximation of the integral ∫abfxdx, where a=3…

Q: 3,2 Evaluate the integral xx + x +2 dx%3D

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Q: The linear approximation to 1 over sqrt(5-x) at x=0 is y=?

A: To find the linear approximation at x = 0 to the function 1/sqrt (5–x).

Q: Evaluate the integral dx (8x + 3)3 by making the appropriate substitution: u = 8х + 3 dx (8x + 3)3…

A: Recall:    ∫un du=un+1n+1+c ; where c is an integration constant.

Q: Explain why the fundin f(2)= 526+ z COSZ - z’e? is entire ?

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Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

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Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: Consider the following BVP: - 2u 1 1sxs2 dx Using boundary condition u(1)-u(2)-0.

A: Sincei have attempted similar problems, let me solve the given problem step by step....

Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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Q: What formula would be used to calculate the middle rectangle approximation of Söy x +2dx using four…

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: Evaluate the double integral dy dx 4. 2.

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Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

Q: 4. Prove 1 < | V1+ a dx <2 0,

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Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: 39.) Show how to use (a) trapezoidal rule and (b) Simpsons rule with n=4 to 4 approximate ſ,"…

A: There are different methods of solving a definite integral without integrating it such as the…

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x*+20x-126x + 2x +3 dx…

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Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

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Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

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: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

Q: 6. y 45

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Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A: