Q3: Evaluate the integral f xe dx by first finding the Maclaurin approximation to the integrand with 3 terms.

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

A: Given information: Concept Used:

Q: Evaluate the integral. (Use C for the constant of integration.) t3 dt V1- t8

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Q: e dy da by reversing the 4-V Evaluate order of integration.

A: Change the limits:

Q: Consider the definite integral. (8x – 1) e- dx Let u = 4x – x. Use the substitution method to…

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Q: Evaluate the integrals in Exercises using integration by parts

A: The integration given to us is  ∫tan-1ydy            (1)

Q: Evaluate the integral or show that it is divergent.

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

A: Given integral is: Using substitution and applying derivative:

Q: Consider the integral -8e-y/2 dy If the integral is divergent, type an upper-case "D". Otherwise,…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt cos²(t) V7 + tan(t)

A: Integration Question

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

A: We use trapezoidal rule ,midpoint rule,simpson's rule to approximate the given integral

Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: the double integral dy dz Evaluate

A: The given integral is: We can solve this integral by changing the order of integration. Consider…

Q: Evaluate the integral.  integral  t 2 sin 2  t dt

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Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

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Q: dx Consider ·S= using rationalizing substitution. x1/2 + x2/3 Find the integrand in terms of z.

A: Given

Q: Evaluate the integrals in Exercises using integration by parts. 3. f cos t dt 4. * sin x dx

A: The formula for an integral ∫udv is uv-∫vdu. Here u function is selected on basis of ILATE order.…

Q: Evaluate the integral -4-2 8x Cos y dy dr y – 4 by reversing the order of integration.

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Q: Evaluate the integral. (Use C for the constant of integration.) t3 In(t) dt C must be in capital…

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Q: Evaluate the iterated integral. V1- x8 dy dx

A: We have to find

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

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Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

A: The given integral is ∫02∫x22ey2dy dx In original integration, the integration order is dy dx. Our…

Q: Find the integral. (Use C for the constant of integration.) [(++ 3)cos( 2 + 6t) at (t + 3)cos( t2…

A: To find the integral

Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

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

A: Given:

Q: Find the integral. (Use C for the constant of integration.) (t + 3)cos t2 + 6t) dt

A: Consider t + 3 as u. Then,

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 а) -dx x² –…

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Q: compute the given approximation to the integral.

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Q: (유) 6. dy dr Evaluate the double integral:

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Q: B)Evaluate the integrals: i) S ii) f/2/2 x 2² siny dz dy dx. rdrde,

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Q: the double integral dy dx Evaluate 2.

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Q: Evaluate the integral. (Hint: u-sub) R/8 S (1+ etan 20) sec² 2x dx O 2e e

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Q: Evaluate the indefinite integral ∫⟨1t,4t3,√t⟩dt, where t>0.

A: We will integrate term by term.

Q: Evaluate the folloming int egrals:- D s secizo tanf2ode 2) S tan' sx dx

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Q: Evaluate the integral 8x cos y dy dr y – 4 by reversing the order of integration.

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Q: Evaluate the integral. "π/4 J.T tan (0) sec²(0) de

A: This question can be solved using integration by substitution.

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

A: To find the integration.

Q: x? Use the residues to evaluate the improper integral: -dx . (x² + 1)(x² + 4)

A: According to the given information, it is required to evaluate the improper integral using residue…

Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Evaluate the integral. (Use C for the constant of integration.) t2 dt 1 - t6

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: Use the specifie substitution to find or evaluate the Integral. (Use C for the constant of…

A: To solve the integration uisng substitution method

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

A: Consider the given integral ∫133xx2+xdx Divide the numerator and denominator by x, get…

Q: Find the general indefinite integral using definition. (3t*-t³+6t²\ a) dt b) S(3 sin x – 4e* + 5* +…

A: Part a,Given,          ∫3t4-t3+6t2t4dt

Q: What is the Laplace transform of the convolution integral of h (t) = sinh 3t u (t), x (t) = cosh(3t)…

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Q: Evaluate the integral. (Use C for the constant of integration.) t5 In(t) dt

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

A: Given:           ∫e2xe2x+3ex+2dx

Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: The upper bound of the error when using Trapezoidal rule to approximate the integral 5 S xe*dx is хе…

A: The given integral is,∫25xe-x dx