Q2:A/ Evaluate the integrals 1 sec²(eVx + 1) dx J Vxe-V

Q: Evaluate the integral. (Use C for the constant of integration.) | 16 In(V) dx

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Q: Evaluate the integral by reversing the order of integration. V3n V3 cos(4x2) dx dy

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Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

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: dx XV 16x4 – 1

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Q: |x| dx 1 X V1– x² -1

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Q: Evaluate the integral. (Use C for the constant of integration.) tan3(x) sec (x) dx

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Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: Evaluate the integral. (Use C for the constant of integration.) 7 V 1- sin(x) dx

A: Evaluating the indefinite integral

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

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Q: Find the inde finite integral. (Use C for the constant of integration.) -5 dx (x2 + + 5)3/2

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Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: dx J (3+ x²)3/2

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Q: Calculate the integral by interchanging the order of integration. 2, (x + 7e – 6) dx ) dy

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Q: Use Property 8 to estimate the value of the integral.

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

A: Given the integral, ∫4tan(x)sec3(x) dx = I(Say) Now, I=∫4tan(x)Sec(x)sec2(x) dx.........(1)  Now…

Q: x2 b) dx Væ³ + 1

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Q: Evaluate the integrals in Exercises using integration by parts.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: Evaluate the integral by reversing the order of integration. 1/2 cos(x) V9 + cos²(x) dx dy…

A: Answer to the question as follows:

Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

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

Q: Evaluate the integral. (Use C for the constant of integration.) 19z3e? dz

A: Explanation of the answer is as follows

Q: The indefinite integral [ 4cotx dx is sinx 4 +C sinx А. В. -4tanx secx +C 4 +C sinx С. D. 4tanx…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan*(x) sec (x) dx

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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 r4-x2 8x cos y dy dx r2 y – 4 by reversing the order of integration.

A: Evaluating the g8iven integral directly is not easy. So if we change the order of integration from…

Q: dx 1 Vx + x3

A: Answer

Q: Evaluate the integral ( Use C for the constant integration) ∫ 11 tan4(x) sec6(x) dx

A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: Use integration by parts to evaluate the integral. 2x In(4x) dx +C

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Q: Evaluate the integral. (Use C for the constant of integration.) 16 In(Vx) dx

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Q: Зх-2 dx%3D V2x+3

A: We need to evaluate the following integral I = ∫3x-22x+3dx                            ........1

Q: Calculate the integral. (Use C for the constant of integration.) dx XV 36x4 – 1

A: Given, ∫dxx36x4-1 We have to evaluate the integral.

Q: First make a substitution and then use integration by parts to evaluate the integral. ecos(t)…

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Q: Evaluate the integral. (Use C for the constant of integration.) 8 tan(x) sec³(x) dx

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Q: Evaluate the integrals below: etanx sec² x 3. a) V(1 – (elanx )2 :. dx, b) / cot5x. dy

A: We need to integrate of the following integrals.

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. ∫ x sec2 x…

A: Consider the given integration as ∫xsec2xdx

Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

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Q: DSX 2 X sec /x dx 3

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Q: dx J 3+1 3+ vx

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Q: -sin20 B)Evaluate the integrals: i) f/2 sinze rdrde, 0 ii) f/2/2 finx 2² siny dz dy dx. 0 0

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Q: Evaluate the integral. (Use C for the constant of integration.) ∫ 3 tan2(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 tan(x)sec^3(x)dx

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Q: 7. f sec5 2 t dt

A: We can solve the integration as below

Q: Evaluate the double integral by reversing the order of integration y* sin(ry²) dydx

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Q: V7y2 - 11 dy y2

A: Given : ∫7y2-11y2dy

Q: Use integration by parts to evaluate the definite integral. 4t2 In(t)dt

A: We have to evaluate ∫1e4t2 ln(t) dt  by using integration by parts.

Q: By using trapezoidal rule for integration find J=Jo' sin' (1/x) dx. n-12

A: The given function is: J=∫07sin31xdx, n=12