1. (x² +y² +z?) ds , where Cis straight line from (1,2,3) to (4,1,4).

Q: (1,6) and perpendicular to 2x+7y=1

A:

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

A:

Q: 1. The line y - 6 = 2(x + 4) passes through which point? OA (-4,-6) O B. (4, −6) Oc( 4, 6) OD (2,6)

A:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: Answer

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0. %3D

A:

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+2t, z = 3+ t.

A: Find the distance from the point (2, 2, 3) to the line x= 0, y=2+2t, z=3+t.

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2 + 2t, z = 3 + t.

A: Given point (2,2,3)and line is x=0 , y=2+2t ,z=3+t.

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: 1. Which points lie on the line 3x – 2y = 12? а. (0, 4) b. (2, - 3) с. 3, d. (0, - 6)

A: Given: 3x-2y=12

Q: The line parallel to y=?x+5, passing through the point (3, 2)

A:

Q: Evaluate |(xy? + 4) ds where C is the portion of the line segment from (1,2) to (3,-4) and then from…

A:

Q: Compute yds where C is the line segment from (1, 2) to (4, 7).

A: We know that,       . Now,

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: