Please see the attached file for the full problem description. --- 1. Transform the given integral in Cartesian coordinates to one in polar coordinates and evaluate the polar integral. : refer to integral 5. 2. Determine the values of the given integrals, where W is the region bounded by the two spheres x^2 + y^2 +
Polar Coordinates and Change Order of Integration; Volume of an Ellipsoid; Change of Variables on Continuous Function of One Variable
Assuming r, θ are the polar coordinates, change the order of integration: ∫-pi/2-->pi/2 ∫0-->a cos θ f(r, θ ) dr dθ Find the volume of the ellipsoid: x^2/a^2 + y^2/b^2 + z^2/c^2 ≤ 1 Let a and b be any numbers such that a^2 + b^2 =1 and f(x,y) be a continuous function of one variable
How Corporations Issue Securities : Interest Rate, Issue Cost and Company Expense, Private Placements and Public Issues
You need to choose between making a public offering and arranging a private placement. In each case the issue involves $10 million face value of 10-year debt. You have the following data for each: A public issue: The interest rate on the debt would be 8.5 percent, and the debt would be issued at face value. The underwriti
∫(pi/2 to 0) sin^4(x) dx -- do not use reduction forumulas use 1-cos2u/2=sin^2x ∫3x^3/sqrt(8-x^2) dx Integrate, integration
Evaluate each of the following integrals: 1. ∫0-->2 6/(5x+2) dx 2. ∫1-->3 e^(-0.4t) dt 3..... 4.... Please see the attached file for the fully formatted problems. Integrate, Integration
Problem 1 and 2: Sketch the region of integration, reverse the order of integration, and evaluate both iterated integrals. ∫0-->2 ∫0-->4-y2 x dx dy ∫0-->pi/2 ∫0-->cosx sin x dy dx Problem 3: When you reverse the order of integration, you should obtain a sum of iterated integrals. Make the r
F(x,y,z)=y ; W is the region bounded by the plane x+y+z=2, the cylinder x^2 + z^2 = 1, and y=0. Integrate the given function over the indicated region W.
1. Using the integral ∫-1-->1 ∫x^2-->1 ∫0-->1-y dz dy dx a) Sketch the region of integration. Write the integral as an equivalent iterated integral in the order: b) dy dz dx c) dx dz dy d) dz dx dy 2. Find the volume of a wedge cut from the cylinder x^2 +y^2 =1 by planes z=-y and z=0. Please show me t
I have a function (see attached). I need to integrate it over m from - infinity to infinity, h from - infinity to infinity. I need to apply a technique such that the integral takes a simple form, easy for integration. The main problem here as you can see is product of terms in the denominator. ---
Inverse Trigonometric Functions (15 Problems), Derivatives (7 Problems) and Definite Integrals (8 Problems)
7.5 Inverse trigonometric functions Find the exact value of the expression. 1) sin^-1 (SQRT3 / 2) 2) arctan(-1) 3) tan^-1 (SQRT 3) 4) cos^-1 (-1) 5) csc^-1 (2) 6) arcsin(-1/ (SQRT 2) 7) sec^-1 (SQRT 2) 8) arccos(cos 2pi) 9) tan^-1 (tan 3pi/4) 10) cos(arcsin ½) 11) sin(2 tan^-1 SQRT 2) 12) cos(tan^-1 (2) + tan
Evalaute the integral 1) ∫ (sin^3 (x)) (cos^2 (x)) dx 2) ∫ ( sin^4 (x)) (cos^5 (x)) dx 3) ∫ ( sin^6 (x)) (cos^3 (x)) dx 4) ∫ ( sin^3 (mx)) dx 5) ∫ (from 0 to pi/2 on top) (cos^2 (theta)) dtheta 6) ∫ (from 0 to pi/2 on top) (sin^2 (2theta)) dtheta 7) ∫ (from 0 to pi on top) (sin
Evaluate the integral using integration by parts with the indicated choices of u and du. 1) ∫ x ln x dx, u=ln x, du=xdx 2) ∫ theta sec^2(theta) dtheta, u=theta, du=sec^2(theta) dtheta Evaluate the integral 1) ∫ x cos 5x dx 2) ∫ (x)(e)^(-x) dx 3) ∫ re^(r/2) dr 4) ∫ t sin 2t dt 5
Please and explain and solve the following: 13. Find the indefinite integral and check the result by differentiation. Integral: x^2(x^3 - 1)^4 dx Answer: (x^3 - 1)^5/15 + C 130. Find the indefinite integral in two ways. Explain any difference in the forms of the answers. Integral: sin x cos x dx
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
Integration : 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
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.