### Double integral

Please see the attached file. Please show me the detailed process.

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Please see the attached file. Please show me the detailed process.

I am not sure how to solve this. Please show all steps. F(x)=ln2x G(x)=lnx Limits: a=1 and b=5

Please show all steps to solve: Domain: 1≤t≤ e^π∕4 ∫4dt∕t(1+ln²t)

Please show all steps to solve: ∫dx∕(x-2)√(x²-4x+3)

The question asks if both of these integrations can be correct and why/why not? a) ∫dx / √1 - x² = -∫-dx/ √1-x² = -cos‾¹x + C b) ∫dx / √1 - x² = ∫-du/√(1 - (-u)²) x = -u dx= -du = ∫-du/√1- u² = cos‾¹u + C

What is the solution? please show each step ∫ dy / (sin‾¹y)√(1 - y²)

How is this solved? Please show the steps ∫√tan‾¹x dx / 1 + x²

How do you solve this integral in the domain shown? Please show each step. domain: ½ ≤ t ≤ 1 ∫ 6dt ∕ √(3 + 4t - 4t²)

What is the solution? Evaluate the integral: ∫dx ∕(x+3)√((x+3)² - 25)

How is this solved? Evaluate the integral: ∫ dx ∕ √(1 - 4x²)

B10. (a) State the Divergence Theorem, being careful to explain any notation you use and any conditions that must apply. The vector field B is given by B = Rcos θ(cos θR - sin θ ^θ ) in spherical polar coordinates (R; θ; φ). This field exists in a region which includes the hemisphere x2 + y2 + z2

Displacement of a body s metres to time t is related by the integral t= ∫r /(g +ks) ds where g k r are constants. Give an expression in terms of r and k for the body to travel distance g/k metres.

Integrate ∫4e ^ -3x dx

Integrate with respect to ∫(5-3e^4x)/e^x dx without using the substitution method.

Evaluate ∫(3-(e^ 4x)) dx limits of 0 and 1 Note! e to the power of 4x as written

Evaluate e to the power of 3x minus 4 divided by e to the power of x between the ordinate limits -2 and -3.

Evaluate 1 divided by 1+4x dx to the ordinate limits 3 and 4.

Integrate 5-3e to the power of4x which is divided by e to the power of x. 4x x trying to write it would be : 5-3e divided by e

Integrate with respect to x (3+4x) to the power -1

1.) compute integral of (3x +5)/((x+1)^2 (x+2)) dx 2.) compute integral from 0 to (pi/2) of (cos x)/(1+ sin x) dx

1.) What is the integral of (x^4 + x^2+1)/(1+x^2)? 2.) What is the integral from 0 to (pi/2) of (cos x)/(1+sin x)?

Dy/dx = x³ - √x + 3 - secxtanx Find y = I got the following answer:y = x4/4 - 2x (3/2)/3 + 3x - secx Is it correct????

Indefinite Integral : ∫x^3 /(x^4 + 1)^3 dx

Integration by Partial Fractions : ∫(2x^3 - 4x^2 + x + 3)/(x-1)^2 dx

Please display every step to finding the answer to the following (S stands for the integral sign): S 1/ (x^2 + 3x -10) dx

Find the integral of a polynomial fraction. See attached file for full problem description.

Use problems 8 and 9 on p. 348 as an outline to write a clear explanation why Simpson's rule is a good way to approximate definite integrals over a finite interval. The questions are attached, I need help explaining each step of the problem, with a few different proofs of how this actually works.

Please solve and explain. Write the expression for the Riemann sum of f(x) = x^2 - 4x on the interval [0,8] with n uniform subintervals using the right hand endpoints of the subintervals. Do not evaluate. Using the Reiman Sum, write the definition of the definite integral 8 to 0 (x^2 - 4x)dx. Do not evaluate. Using

Please explain and solve the shaded problems.

Evaluate the integrals using the following values (i) For integral 4 on the top, 2 on the bottom x^3 dx = 60 (ii) For the integral 4 on the top, 2 on the bottom x dx = 6 (iii) For the integral 4 on the top, 2 on the bottom dx = 2