# Find th length of th line x = int sqrt(sec(t)^4 - 1)) from 0 to y

• chewy
In summary, the problem asks to find the length of a line using a definite integral. The equation involves a square root and a trigonometric function. The limits of integration are given as -pi/4 and pi/4. The solution requires substitution and the use of trigonometric identities. The final answer is 2 times the integral from 0 to pi/4. The individual who posted the question eventually figured out the solution.
chewy

## Homework Statement

definate integral to find length of line

x = int [sqrt( (sec t)^4 - 1)
integrate from 0 to y with -pi/4 < y > pi/4
it is actually y is equal or more/less than pi/4

## The Attempt at a Solution

Ive worked out that the length of the line will be the same from -pi/4 to 0 as 0 to pi/4,
giving me

x = 2*int(sqrt( (sec t)^4 - 1)
integrating from 0 to pi/4,
im struggling with the integral, i know it must be substitution and i ve tried numerous trig identities just been coming up blank so far. a little push in the right direction would be great

sorry that was meant to be y is equal or more than -pi/4 and y is equal or less that pi/4

dont worry about it i figured it out

## 1. What does the equation x = int sqrt(sec(t)^4 - 1)) from 0 to y represent?

The equation represents the length of a line on a graph, where x represents the horizontal axis and y represents the vertical axis. The line starts at the point (0,0) and ends at the point (y,x), with the length being the integral of the square root of the difference between the secant of t raised to the fourth power and 1.

## 2. How is the length of the line calculated in this equation?

The length of the line is calculated by taking the integral of the square root of the difference between the secant of t raised to the fourth power and 1, from 0 to y on the y-axis.

## 3. What does the "int" notation in the equation stand for?

The "int" notation in the equation stands for the integral or the area under the curve of the function being integrated.

## 4. Can this equation be used to find the length of curved lines?

No, this equation can only be used to find the length of straight lines on a graph. It cannot accurately calculate the length of curved lines.

## 5. Is there a specific unit of measurement for the length in this equation?

The unit of measurement for the length in this equation will depend on the units used for the x and y axes. If the x and y axes are measured in meters, then the length will also be in meters. It is important to make sure that the units for x and y are consistent in order to get an accurate measurement of the length.

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