Evaluate the line integral H.dr, where H (4xy, 4 – x², z²) and C is an arc of a circle in the z = 3 plane, centred on the z-axis, with radius of 2. C is the arc is from the point (2,0, 3) to (√2, √√2, 3).

Q: the circle is the tangent to both x and y axis. A point on the circle is (2,1). Calculate the area…

A: This question is based on Circle.

Q: FADEFIS an isosceles triangle with base DF, what is the value of x?

A: Given triangle DEF is an isosceles triangle with the base DF.Soa)DE = EF5x - 3 = 3x + 75x - 3x =…

Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: $ Evaluate clockwise. positiver sin z 22 +1 dz where y is circle C(0, 2) traversed once and counter-

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Q: 5. Sketch the circles x + y = why the circles must be internally tangent. (Hint: Find the two radii…

A: Given: i. x2+y2=225ii. x-62+y-82=25 To Find: Sketch the given circles and explain why the circles…

Q: Which projection of (cost, cos 2t,sin t) is a circle?

A: Which projection of (cost, cos 2t,sin t) is a circle?

Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

Q: Let f(2) = 77, 0 = 0, A = 8 and B = 8+8i. Let C, be the contour composed of the line segments OA and…

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Q: Evaluate F. dr along the line segment C from Pto Q. F = -8 xi+5y j; P(-1,0), Q(7, 0) F. dr i

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Q: Find the distance d between the two parallel planes x + 2y 2z = −2 and x + 2y = 2z = 1.

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Q: Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=D0

A: Area of the circle = 9π sq.units

Q: Evaluate zdz from z=0 to z-4+3i along the curve C given by the line from z=0 to z=3i and then the…

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Q: Find the distance in between the point P(0, 2, – 1) and the point Q(0, 1, 2).

A: we have to find distance between the points P and Q Given Points : P(0,2,-1) and Q(0,1,2)