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Integral Calculus 2 Handout

This document contains review problems related to calculating lengths of curves using integral calculus. It includes 6 multiple choice questions calculating lengths of arcs along curves defined by rectangular coordinates, polar coordinates, and parametric equations. It also contains 3 additional practice problems calculating lengths along curves defined by common equations like a parabola, circle, and cable suspended in a parabolic shape.

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Justine Ejay Moscosa
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176 views1 page

Integral Calculus 2 Handout

This document contains review problems related to calculating lengths of curves using integral calculus. It includes 6 multiple choice questions calculating lengths of arcs along curves defined by rectangular coordinates, polar coordinates, and parametric equations. It also contains 3 additional practice problems calculating lengths along curves defined by common equations like a parabola, circle, and cable suspended in a parabolic shape.

Uploaded by

Justine Ejay Moscosa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Civil Engineering November 2020 Review Innovations Integral Calculus 2

50 m
LENGTH OF ARC
Rectangular Coordinates 4m B
(ds)2  (dx)2  ( dy )2
A
2 2 6m
x2  dy 
s= x1
1    dx
 dx  A. 55.8 m C. 56.81 m
2 B. 60 m D. 53.27 m
y2  dx  ds

dy
s= 1    dy 4. Find the length in the first quadrant portion of
1
y1
 dy  dx the curve x2 = 16 – 8y. 4.59
5. Find the length of the arc of one branch of the
parabola y2 = 4x from the vertex to the end of
Polar Curves the latus rectum. Ans. 2.296

2
6. A point moves in a plane according to the law
2  dr  x = 1 – cos 2t and y = 2 cos t. Find the length

2
s= r    d r = f()
1  d  of the path. Ans. 5.916
P2(r2, 2)

dsc dr
r ds
d
P1(r1, 1)

Problems

1. The length of arc of the function y = x2/3 from


x = 0 to x = 8 is:
A. 8.765 C. 10.231
B. 9.073 D. 12.988
2. What is the perimeter of the curve r = 4(1  sin
)?
A. 32.00 C. 25.13
B. 30.12 D. 28.54

3. A cable carrying a uniform weight is


suspended in a parabolic shape as shown.
Determine the length of the cable.

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