Consider the graph of the function g(x): 4 y = g(x) 2- The graph from x = 2 to x = 6 is a semicircle. Evaluate the following integrals by interpreting them in terms of areas: (a) | g(x) da =| (b) 9(x) dx 7 (c) | g(x) dx 4.

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

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Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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Q: Evaluate the integral. (Use C for the constant of integration.) | (x2 - x) dx

A: We can solve the indefinite integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

A: Given ∫8xx+c5dx

Q: Evaluate the integral. (Use C for the constant of integration.) dx - x2

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Q: Evaluate the integral. (Use C for the constant of integration.) (x2 + 2x) cos(x) dx

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Q: Evaluate the integral ,(1 – x – 4x³ + 2x³) dx a) Analytically b) Single application of trapezoidal…

A: we have  f(x)=1-x-4x3+2x5 we need to find ∫-24f(x)dx  a) analytically b) using trapezoidal rule

Q: Evaluate the integral. (Use C for the constant of integration.) 8 dx x + 8 +

A: We first rationalize the…

Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

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Q: Evaluate the integral. (Use C for the constant of integration.) x² + 9x + 1 dx (x² + 1)2

A: Make two parts of the integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 10x2 cos(mx) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: Use residues to evaluate the improper integral [a+x2/1+x4]0∞dx; where a is a real constant

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Q: Q7. Using Simpson's Rule evaluate the integral √² √1+xª dx using 8 subintervals.

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 7x + 1 dx (x2 + 1)2

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Q: Use the tabular method to find the integral. x²(x – 2)/2 dx

A: Use tabular method to find the integral  ∫x^2(x-2)12dx sign Derivative Antiderivative + x2…

Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

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Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: Evaluate the integral. (Use C for the constant of integration.) (x6 − 6x2)4(x5 − 2x) dx

A: From the given problem:   I=∫x6− 6x24x5 − 2x dx...(1)   First simplifying:…

Q: Evaluate the integral. (Use C for the constant of integration.) 9x cos(8x) dx

A: Integrate this by integration by parts

Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0)…

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

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Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x + 20x + 104

A: Consider the provided integral, ∫x+21x2+20x+104dx Evaluate the provided integral. Apply the…

Q: Evaluate the integral 11-x²4-x²-y !!! 0 3 x dz dy.dx.

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Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 25 – x2

A: Let, Integrate using substitution,

Q: Evaluate the integral. (Use C for the constant of integration.) 3e3x dx

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

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Q: Evaluate the integral. (Use C for the constant of integration.) 17xe2x dx (1 + 2x)?

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Q: Evaluate the integral. (Use C for the constant of integration.) sin (x) cos (x) dx 4.

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Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

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Q: Evaluate the integral. (Use C for the constant of integration.) 8x 8 dx 8x e

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) dx x2…

A: Given: ∫dxx24x2+81

Q: Evaluate the integral. (Use C for the constant of integration.) 3 + 2x - x2 dx

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral 13 In(x)…

A: (1) The trapezoidal rule gives: So, T12≈2.0810

Q: Evaluate the integral. /9-x2 dy dx dz = /9-x2 (x² + y²)!/2 3 J

A: Straightway, without any further delay, please convert to cylindrical coordinates: x = rcost; y =…

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: To find the integration.

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

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Q: Evaluate the integral. (Use C for the constant of integration.) 7-6x - x² dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: consider the function y (x) = ln (x), from (1,0) to (3, ln (3)) b) Set up the integral that…

A: Setting up the integral

Q: Use the Midpoint Rule with n = 4 to approximate the integral. 10 x² dx M4 =

A: The given integral is ∫210x2dx. The mid point rule states that if fxis continuous on [a,b][. Let n…

Q: Consider the graph of the function g(x): yA y = g(x) -2- 4 The graph from x = 2 to x = 6 is a…

A: Given, The graph of y = g(x) The graph of y=g(x) is a semi-circle from x=2 to x=6

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n34, also find ET…

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Q: Evaluate the integral. ( Use C for the constant of integration. )

A: The given integral is ∫x+21x2+20x+104dx. Evaluate as follows.

Q: Evaluate the integral. (Use C for the constant of integration.) 5x cos(4x) dx

A: Given, ∫5xcos4xdx We have to evaluate the integral.

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: Roro is looking at the iterated integral (x² + y²) dx dy and suggest to Mpho that the integral does…

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