Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

Q: Line segment t and line segment r are parallel. Both line segments are reflected across the y-axis…

A: We have to find the distance between line segments t' and r'

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: 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: 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: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: The curve y = sqrt ( 4 - x sq. )  ,-1 < = x < = 1  , is an arc of the circle x sq. +  y sq. =…

A:

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: Evaluate the line integral Say ds, where C is the right half of the circle æ² + y² = 4.

A: We have to evaluate:∫C8xy6dsHere C is the right half of the circle x2+y2=4.

Q: Evaluate [F.dr, where C is the circle x² + y² = 4 oriented counterclockwise and F = (y,-x). Set up…

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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

A:

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: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

A:

Q: e Lay xy¹ ds where C' is the right half of the circle x² + y² = 9 Evaluate

A: We find required integral by parametrizing x and y .