3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region in the xz-plane bounded by z = 2x, z = 5, and x = 0. | (12y – 8x) dV

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A:

Q: Q3: What is the answer of the double integral of the f (x, y) = 4x+2 over the region x^2<ys2x, and…

A: According to question, Given function,fx, y = 4x+2,x2 ≤y≤2x,0 ≤x ≤ 2

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: Evaluate the double integral / (a (x² ,2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

A:

Q: Write down the new limits of integration for the integral -1 -1-y IIL" S(7,4, 2) dz dy dæ if the…

A: As per given tripple integral  0  ≤  z  ≤  (1 - y)  x2  ≤  y  ≤  1  -1  ≤  x  ≤  1   Thus, curves…

Q: 12) Find +he integral of the f(xiyia)=x+y? function on the region between the x4y1 and x?+y"= 9…

A: Convert the integral in cylindrical coordinate: ∭Vfx,y,zdxdydz=∫z=01∬1≤x2+y2≤9x2+y2dxdydz…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

A:

Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

A:

Q: Which of the below double integrals has the following region? -1 5 4 3- 2 -1 0 Select one: None of…

A:

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: Evaluate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x > 0

A:

Q: Evaluate the integral: ∭D(x2+y2+z2) dxdydz, where D is defined by x2+y2+z2≤2.

A: Given:-                               Evaluate the integral: ∭Dx2+y2+z2dxdydz…

Q: 7. Evaluate the line integral by using Green's Theorem feve'dx +2e*dy C is the rectangle with…

A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

A:

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

A:

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

A:

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

A:

Q: 1) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

A:

Q: Sketch. the.region.cf.integratizin.and.evaluabe. thaw .. fallowing. integrals a ..... in2 Ins 2X-년…

A:

Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

A:

Q: Evaluate the triple integral, 2xy dV, where the intergral is bounded by the parabolic cylinders y =…

A: The given triple integral,

Q: Suppose that f(x, y) = 7x + ly at which {(x, y) | – 4 < a < 3, – 4 < y< 3}. D Then the double…

A:

Q: Use Green's Theorem to evaluate the line integral of C to the function (y − x) dx + (2x − y) dy  for…

A: To evaluate: ∫Cy-xdx+2x-ydy using Green's theorem where C is the boundary of the region lying…

Q: 25. Evaluate the integrals. (a) |(*+y) d4, D bounded y =Vx and y= x. (b) [[[yz cos(x' HV where E =…

A:

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

A:

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: 3. Show that, in the region D: 1< x<e, 0<y<In(x), the following double integral 3e4 + 1 x3 dA 16

A:

Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

A:

Q: 2. Show that, in the region D: 0 < x<1, 0 <y< x², the following double integral 1 dA =- In(2) x5 + 1…

A:

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: Suppose that f(x, y) = e² / Y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D Then the double…

A:

Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

A:

Q: Evaluate the following sum of iterated double integrals: 1 2y r2 r4-2y dz-a dx dy + Ax-a² dx dy e…

A:

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A:

Q: Evaluate the following integral. JJ. xyz dV if S is the region bounded by the cylinders x² + y² =…

A:

Q: 2. Evaluate the iterated integrals by (i) viewing R as a type I region, and/or (ii) viewing R as a…

A:

Q: Set up the iterated double integral 9-9x SS dy dx of x 1. the limits . the limits of y

A:

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

A:

Q: Evaluate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x 2 0

A: Consider the following graph:

Q: Set up the definite integral that gives the area of the shaded region bounded by the graphs of y,…

A:

Q: Suppose that f(c, y): at which {(x, y) | 0 s< 1, - a <yS vE}. 1+ x Then the double integral of f(x,…

A: According to question given that f(x,y)=y1+x at which {x,y) |0≤x≤1, -x≤y≤x

Q: 2.) stote the double integral J (x_ yt) dxdy where R is the region R bounded by Ixl+ lyl s 7 in with…

A:

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A:

Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.