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Integrals

Double integral

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

Area between two curves

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

Integration

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

Inverse trig integration

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate integral

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

Multiple Integrals, Vector Fields, Hemispheres and Divergence Theorem

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

Integration

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

Integration

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

Integration

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

Antiderivative

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????

Partial Fractions

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

Simpson's Rule

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.

Integration

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

4 Definite Integrals

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