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Complete explanation of integration problems

Solve. Show all the steps. If you use software to complete it, explain to me what steps are needed to find the solution, (I can easily input the problem into Maple myself). integral (1/(cos^4)7x)dx

Integration by parts

In this problem I am asked to use integration by parts utilizing the formula: ∫udv = uv - ∫vdu Please show the values of u, dv, du, and v and the steps to achieve the solution. Thank you. ∫x²sinx dx

Surface Area of a Revolving Curve

Using the formula for the surface area of a revolving curve about the y-axis: S=∫2πx√(1 + (dx/dy)²)dy throughout a,b Find the area of the surface generated by revolving the curve about the y axis within the given boundaries x=√(2y-1) 5/8≤y≤1 the revolving base passes thr

Surface Area of a Revolved Curve

Utilise the following formula that gives the surface area of a curve that revolves around the y-axis: S=∫2πx√(1 + (dx/dy)²)dy throughout c, d Now calculate the area of the surface that would come about by rotating the curve around the y axis with the boundaries below: x = (1/3)y³′² - y ¹&#824

Area between two curves

The area I am looking for is the region bounded by the two functions y=x² and y=2-x between the limits (2,0) and (0,0) and bounded by the x axis and the point y=1 What is the area between these two curves? Using the formula A=∫f(x)-g(x)dx

Riemann Sum Area Between Two Curves

Using the Riemann sum formula: A = ∫ [f(x) - g(x)]dx from a to b Find the area between y=1/2sec²t and y= -4sin²t between the points π∕3 and - π∕3 Please show a detailed solution. Thank you.

Multiple integration

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 +

Evaluate the Definite Integrals

∫(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 the Integrals (4 Problems)

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

Triple integral

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.


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. ---

Integration : Trigonometric Integrals and Integrate by Substitution

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

Integration by Substitution

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

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


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)