Convert to polar coordinates in the xz-plane, similar to Example 3 in the book. r2 63 – 2x? – 2z? – (5x² + 5z²) dz dx = | (V9-x2) Volume = 63- 7r^2 Σ dr de. where 0, = Σ 02 Σ r2 = pi II M M M

Q: Find an equation for the paraboloid z = 3 – (x² + y) in cylindrical coordinates. (Type theta for 0…

A: The given equation of the paraboloid is: z=3-x2+y2 To find the equation of the paraboloid in…

Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

A:

Q: Consider the parametric equation of the shifted ellipse 9 45 x = 4 cos 0, y = 16 sin e Evaluate the…

A:

Q: c3 9-22 J. 3. Sketch the region, convert the integral (x2+y²)²dydx into polar coordinates and…

A: Use polar coordinates

Q: An ellipsoid S has the parametric equation S (0, ) = (cos0 sinø, 2sino sinø, 4cos ø) where O and…

A:

Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: →cos(nπ) = (-1)n  →First find the inital co-ordinates at t = 0. Now, we have to find the time at…

Q: V18-x2-y Convert (x² + y + z?)dzdxdy into spherical coordinates. 2n/3 3V2 4 p* cos pdpdpdO /2 -n/2

A:

Q: 31. Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 1 and z = 4x²…

A: Given x2+y2=1 & z=4x2 x2+y2=1 is the equation of circle. That is x2+y2=12,  Therefore, Radius is…

Q: When transforming polar coordinates S sinx²+y²) dydx _ the binary integral يصبح بالشكل Z csc(8)…

A: Using polar coordinates

Q: 2= 25 -1st<0 is rotated about x-axis. Find the surface area of the obtained The parametric curve…

A:

Q: 8-a2-y By converting to spherical coordinates, evaluate 2² dz dx dy

A: Let us consider the rectangular coordinates (x,y,z) then the relation between spherical coordinate…

Q: 4-x² –y² b.) z dz dy dx -VI¬x² J /3x²+3y? from Cartesian coordinates to spherical coordinates.

A: We need to find the geometry of the given integral.  Then find the limits in terms of spherical…

Q: 3. Consider the curve y = x°, 0<x < 3. (a) Find parametric equations for the surface obtained by…

A:

Q: 4. (i) Use the parametric equations of an ellipse, x = a cos (t) , y = b sin (t), 0 < t 2m, to find…

A:

Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

A:

Q: 103. Show that the parametrization of the ellipse by the angle 0 is ab cos 0 X = a² sin² e + b² cos²…

A: From given data,

Q: For spherical polar coordinate system (3² exp(x)sin Cosø 4/2 `a 1 -Zr,„Zr. 2a a |W„Y„dV = 8¸ = ? px…

A:

Q: Find the slope of the polar curve r = 2( 1 – cosx ) when x = pi/4 . a. 1.707 b. 2.414 c. 1.866 d.…

A: Given equation of curve : r=21-cosx   ,  x=π4. drdx=2sinx The slope of polar curve   r=21-cosx  at…

Q: Find an equation of the form p = ƒ (0, 4) in spherical coordinates for the surface z = 16 (Use…

A: The equation in spherical coordinates for the surface is determined as shown below

Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

A: Given r=4cos2θ and 0≤θ≤π4 To find the area of the surface formed by revolving the polar equation…

Q: For spherical polar coordinate system 1 Z -Zr Zr 3/2 4/2 a exp(-()sin OCoso 2a px a V WmdV = 8 = ?…

A:

Q: 3. Consider the curve y = x³, 0 < x < 3. (a) Find parametric equations for the surface obtained by…

A:

Q: 25-r2 Evaluate (x2 + y?)3 dy dx by converting to polar coordinates.

A: we have to evaluate the following

Q: Find the area enclosed by the simple closed curve given by the parametric equations, x = 2cost +…

A: *to find:- total area.

Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

A:

Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

A:

Q: Find an equation for the paraboloid z = x2 + y2 in spherical coordinates. (Enter rho, phi and theta…

A: The equation of the paraboloid z = x2+y2                                       ........(1) To…

Q: 4-22-y2 Compute y? Vx2 +y? + z² dz dx dy by converting to spherical 4-x2- coordinates.

A:

Q: Use spherical coordinates to evaluate V4-x² 4-x²-y² + y² + z² dz dy dx V4-2² Jo Do not forget to…

A:

Q: 29. Find parametric equations for the tangent line to the cur ve of intersection of the paraboloid z…

A: Given paraboloid is z=x2+y2 ellipsoid is x2+4y2+z2=9 and the point (1,-1,2) find the parametric…

Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations.     x=(t-2)5/2…

A:

Q: 4. y = sin2r, 0 sa Find the area of the surface of rotation obtained by rotating the curved segment…

A:

Q: Q5) Evaluating in polar coordinates: *+ y*)dydx

A:

Q: Test for symmetry and graph polar equation

A:

Q: 9. (a) Find the equation of the cone 3.x2 +3y2 in spherical polar coordinates. (b) Use spherical…

A: Given

Q: iyı , Z2 = x2 +iy2 than Z,Z, in polar forr + 62) – i sin(0, + 02) Z,Z2 = ir2(cos(0, – 02) + i sin O…

A:

Q: 2 V4-2 Using polar coordinates, evaluate dydx =? 100 -2 OA (1/50)mfe? +1) OB 3/ 50)fe +1) - (1 /…

A:

Q: V16-x2 Use polar coordinate to evaluate 2 dy dx . Vx² +y² Leave your answer correct to two decimal…

A: To evaluate the given double integral apply the following formulas  x= r cosθ y = r sinθ x2+y2 =r2…

Q: Consider the parametric equations t3 + 2t, y = e' +t te [1, 10] Find an integral expression for the…

A:

Q: 6. a. Find the length of the curve using the equation 12xy = 4x4 +3, from x = 1 to x = 3. b.…

A:

Q: Converting 4-y2 4-y2 2² +y? f(x, Y, z)dV into polar coordinates gives

A:

Q: Find two parametric representations for the part of the ellipsoid 2x + y° + 22- 17 thất lieš tő thé…

A: Given:2x2+y2+2z2=17

Q: Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface…

A:

Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

A:

Q: 37. The polar equation of the curve is expressed as r-2sine + 2 cose.. Compute the area bounded by…

A:

Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

A:

Q: 2 Evaluate V4-x? Jo J2- dy dx using polar V 2x-x2 Coordinates.

A: Solution:-

Q: V2 Evaluate x² dy dx by changing /4- to polar coordinates. Select one: O a. T A – а. л — 2 О. 2л — 6…

A: Given: ∫02 ∫-4-x2-x  x2  dy dx Evaluate the given integral by changing