d. Integrate your integrals from parts c and d and show that the two integrals give the same area.

Q: Evaluate the integral LT :(+y°)etzc>xcy = ?

A: In this question, we have to evaluate the given triple integral. The iterated form of integral is…

Q: 5) Use an iterated integral to find the area if the region. y y = 4– x2 3 2+ 1 3 4

A:

Q: Use an iterated integral to represent the area of the rectangle shown in Figure 1 Rectangular region…

A: The given question is taken from the calculus in which we have to represent the area of the given…

Q: Evaluate the integrals

A:

Q: S 343.4 * (0) (9x) dy

A:

Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: SoSs, e dxdy = Evaluate the integral by reversing the order of integration. et? 8-

A:

Q: Evaluate the integral where E is the region over the part of the ball delined by dU=P

A: To evaluate ∫∫∫Ezx2+y2+z2-32dV and E is the region x2+y2+z2≤16 and z≥2 Given…

Q: evaluate the integral using the Integration by Parts formula with the given choice of u and dv.

A:

Q: Choose z = x to transform the integral to a new integral in the variable z and evaluate the new…

A:

Q: Use a double integral to find the area of the region one loop of the rose: r = 7cos(3θ)

A: Given : r = 7cos(3θ)

Q: 1. Evaluate the integral and sketch the region of integration fo S e-rro drd0

A: Definition used -              Double integral with polar coordinate -…

Q: B. Set up the integral for the area enclosed by y = 5x – x² and y = x from x =-2 to 6. Do not solve.

A:

Q: For the given integral, draw the region of the integration, reverse the order of integration to…

A: We need to reverse the order of integration for the following integral ∫01∫x2xfx,ydydx

Q: Sketch the region of integration, reverse the order of integration (if needed), and evaluate the…

A:

Q: Evaluate the integral. In(x) dx, y > 0

A:

Q: Evaluate the integrals in Exercises using integration by parts

A: Since you have posted more than one question, we answer the first question for you. For the other…

Q: 1. xe 2* dx; u = x, dv = e 2× dx

A:

Q: Evaluate the integral by interpreting it in terms of areas.  integral 0  to 9  (1/3 -2)dx

A: given that integral 0  to 9  (1/3 -2)dx We need to evaluate the integral by interpreting it in terms…

Q: Use a double integral to find the area enclosed by one loop of the four-leaved rose r = cos 20.

A:

Q: The value of the iterated integralS, L (3 - ry)dydx=.. 2

A: Given: ∫-24∫013-xydydx

Q: Sketch the region D that gives rise to the following repeated integral, change the order of…

A: Given: ∫01∫x1siny3+12dydx. To Find: (i). Sketch the region. (ii). Change the order of integration…

Q: the exaet V alde Of the integral. a

A: The objective is to show the exact value for the integral, ∫01axdx This can be re written as,…

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 2 In…

A:

Q: Evaluate / av1 – aª dæ by making a substitution and interpreting the resulting integral in terms of…

A: Firstly we will find the definite integral after that fill the limit  I =  ∫ x*sqrt(1-x4) dx…

Q: Use a double integral to find the area of the shaded region. 7/2 20 r= 9+9 cos e 10 - 10 -5 5 10 15…

A:

Q: 4. Evaluate S,(x + 3)v4 – x² dx by writing it as a sum of two integrals and interpreting one of…

A: Given integral is ∫−22x+34−x2dx First , we will write the given integral into sum of the two…

Q: Evaluate the integral using Integration by Parts. | 3y? sin 4y dy

A: Here we have to evaluate the given integral by using integration by parts.

Q: The value of integral .dz is (z – 1)?

A:

Q: y. x= y? – 2 y = 1 x= e" y =-1

A: Given the graph of a region

Q: Reverse the order of integratlon and then evaluate the Integral 10Tin6 Jinu! dx dy 9/10 et2

A:

Q: b) Determine the volume of D = 5[ 1 dV using integral -zx.

A: The volume of a solid V is given by V=∬∫v 1 dvwhere limits of x,y and z can be found from the given…

Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: Determine the parts U Ind du for the following integral XVX-3 dx

A: Given query is to find the integration using substitution.

Q: 1. dæ; u = x, dv = e2¤ dx

A:

Q: Use a double integral to find the EXACT area enclosed by the graph of r = 3+3 cos 0. 8=1/2

A:

Q: Express D as a union of regions of type I or type II and evaluate the integral.57.∬Dx2 dA

A: Use the following properties of integral and the formulae, to obtain the result. The equation of…

Q: Sketch the region D that gives rise to the following repeated integral, change the order of…

A: first we will sketch the bounded region corresponding to the given integration. then bye doing…

Q: Evaluate the integral by reversing the order of integrati 2 r6 I 7e dx dy 3y

A:

Q: Use a double integral to find the area of one loop of the rose r = 2 cos(30).

A:

Q: (b) Evaluate uV1 – uª du. by making a substitution and interpreting the resulting integral in terms…

A:

Q: 32. Sketch the negion whose area is given by the de finite integral ST-x* dx. Then use a geometric…

A: The graph is shown below:

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

A:

Q: Write five other iterated integrals that are equal to S, L f(x,y,z)dz dx dy.

A:

Q: g(x) = [ (1 + vf) dt

A:

Q: Compute the indicated integral by findng the area of the trapezoidal figure below. 110 4,0 F1 10 •5…

A: Given: A=∫35x+3dx

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

A:

Q: Consider the area between the graphs x + 2y = 29 and x + 6 = y?. This area can be computed in two…

A:

Q: 1–q² (b) Interpret Vr2 + y? dydx as a volume and calculate the integral without integrating.

A: b)

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.