For questions 49 a and b, Each integral represents the volume of a solid of revolution. Describe the solid. а) sin? z dx 0, b) (xª – 2º) dx -

Q: Evaluate the triple integral ] 12z(x?+y?) dV, where G is the solid hemisphere x2+ y² +z? <1, z 20. 4…

A:

Q: The improper integral A) 0 B 1 C D e +∞o Sto 0 8 ex dx is

A: On solving this we will get

Q: Evaluate the integral, AP where, E lies between spheres +y + z = 2 and a + y + = 3. for a 20

A:

Q: Use the Table of Integrals  toevaluate the integral

A:

Q: Eva lua te the integral (1+z)e² Sinz dz, where C: |z|=1, by any two me thods and compare the…

A:

Q: The improper integral A) 0 B 1 C D) e 8 ·+∞o Ste ex dx is

A:

Q: Find the best order and evaluate the integral Sla x sec? xy dA; R = {(x,y): 0 < x < , 0<y< 1}.

A:

Q: Each integral represents the volume of a solid. Describe each solid

A:

Q: From the basic definition of complex integration, evaluate the integral o f(z) dz, where C is the…

A: Let us parametrize C: the unit circle enclosing the origin by z=eit. Here, f(z)=z2. Now, we need to…

Q: Find the surface area of the solid generated by revolving the cycloid x= a(0- sin g). y =a(1-cos ).…

A: We have to find the surface area of the solid generated by revolving the following cycloid about the…

Q: Evaluate the integral / sin (9x? + 4y?)dA, where R is the region in the first quadrant R bounded by…

A:

Q: e the definite integral that represents the area of the surface generated by revolving the cur x3 y…

A:

Q: The area of the surface obtained by revolving the curve x= Vy+3 for a-3.) 2x /4y + 12 dy 2л уу +3 dy…

A: Consider the curve x=y+3 for a≤y≤b. Find the area of surface when curve is rotated about y-axis.…

Q: SSS (x+ yz?) dx dy dz v. 06x< !, 0£ys2

A: Given that ∫∫v∫x+yz2dxdydz, where v:0≤x≤1, 0≤y≤2, -1≤z≤3 Here, we will evaluate the given integral

Q: Evaluate the triple integral S" S, sin y² dz dy dx.

A: We need to find the triple integral ∫03∫0π∫0ysiny2dzdydx. So,…

Q: Evaluate the iterated integral: 24xyz? dx dy dz

A:

Q: If a € R+, which of the following expressions or triple integrals is NOT equal to the volume of a…

A: We want to find integral which does not represent the volume.

Q: Calculate the integral approximations T6 and M6 for ∫sec^2x dx [0,pi/7]

A:

Q: The integral 4x2 + 4y? + 422 dV V = MA, where R is the solid hemisphere with x? + y? + 22 0 Find the…

A: Find your answer below

Q: lEvaluate the integral ×+ス de . x²+2x linlx?Cx+z)e X+2 (x+2)²|&7C Dinlx (x+2)I +c E) Inl x て) 12

A: Topic = Integration

Q: For questions 47 a and b A solid is obtained by rotating the shaded region about the specified line.…

A: Integral set up of the given bounded region using Shell Method:     Shell Method: Volume =…

Q: The value of the integral oIm(iz)dz, where C:| z|= 2, counterclockwise, is

A:

Q: )Find the volume of the solid obtained by rotating the sine function between x 0 and x t about the…

A:

Q: Evaluate the following integral. ||2x sec?y dA; R=(x.y): 0sysx?, 0sxs- 2 R 2x sec y dA = (Type an…

A:

Q: The integral /4x? + 4y? + 42² dV тп, R where R is the solid hemisphere with x? + y? + z² 0 Find the…

A:

Q: For what value. of4, the fundion Ux)= I+dx is. solution of %3D the integral equation x3= Ut dt

A: We have to first transform the x variable of u function to t.

Q: 6. The volume (in ft') of a sphere with radius 2 feet is given by the integral a,2-x' dx a. TC 7[…

A:

Q: LL L dx dy dz 4. Evaluate the triple integral :

A: First Evaluate integration w r to x  Second integration w r to y Third integration w r to z

Q: Evaluate the integral Ur (x² – 2y²) dA, where R is the first quadrant region between the circles of…

A:

Q: Find the equation to solve the surface area obtained by revolving the parabola x? = 4y from x = -2…

A: If is a function, then the independent variable x is called the input of the function and the…

Q: Consider the equation. g(x) h(y) dA = g(x) h(y) dy ) dx = dy dx Use the above equation to evaluate…

A: Just I have used the given rule of double integration and using some formula of integration and get…

Q: Evaluate the integral, (x - y) dV E where, E lies between spheres r + y? + z2 = 1 and r + y² + 2? =…

A: Evaluate the integral ∭Ex−ydV, where E lies between spheres x2+y2+z2=1 and x2+y2+z2=2 for y≥0. For…

Q: Evaluate the double integral /| sin(z² + y*)dA where D is the bottom half of the circle x2 + y² = T.…

A:

Q: The length L of the curve 4y? = (4x – 3)3, 2 0, is given by the integral, .3 Ax² + Bx + C dx 2 and…

A: It is given that - The length L of the curve - 4y2=(4x-3)3  , 2≤x≤3where y≥0 is given by the…

Q: Given that D=p²z?sina,C/m², calculate the total charge enclosed by a cylinder with radius = R1 meter…

A: Total charge enclosed = volume integral (volume charge density dv) volume charge density =…

Q: The value of the integral xdz, where C: Iz| =1 is C O a. Ob. 0 O C. iT O d. 2mi

A: The integrand 'x' is analytic inside the curve |z|=1 so the integral will be zero for the closed…

Q: 47. Evaluate the integral , Vx² + y² dA, where R is the region inside the upper semicircle of radius…

A:

Q: What does the following integral calculate? f(x, y, z)dV E

A:

Q: - dx dz dy . x² +z? Evaluate the iterated triple integral

A: To evaluate the triple integral: ∫02∫0y∫0z3zx2+z2dx dz dy

Q: The arc length along the parabola y = x from (1,1) to (2,4) is given by which of the following…

A:

Q: Calculate the volume of spherical object below by using differential elements if radius is r, 0 < 0…

A: The spherical object is given by To evaluate : The volume of the object.

Q: Evaluate the triple integral. SI. {(x, v, z) | 0 < y s 2, 0 < x < V4 - y?, 0 < z < 5y} 2x dV, where…

A:

Q: Evaluate the iterated integral. 5x 15x? sin y dy dz dx Jo

A: Given ∫0π∫05x∫0xz15x2sinydydzdx Evaluate the iterated integral

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t – sin(t), y = 1 -…

A: Given cycloid, x=t-sint, y=1-cost and area is given by A=∮Cxdy-∮Cydx=12∮Cxdy-ydx

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: Evaluate the given integral (2z+1) dz where the contour C is given in the figure,

A: In this question, we use the path for the integral  ∫C(2z+1)dz where C is the path given in the…

Q: up, but do not evaluate, an Integral for the length of the curve. y = 7 cos(x), 0 < x < 2n dx

A:

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A: Area under one arch of the cycloid is

Q: Given the area bounded by the parabola x– 4x + 12y - 20 = 0, the x-axis and the lines x = 1 and x =…

A: ∫ (y^2)dx is the formula for moment of inertia