How do you find the length of the curve #y=lnabs(secx)# from #0<=x<=pi/4#?

Answer 1

#ln(sqrt2+1)=0.8814# length units, nearly..

In the given interval,# |secx|=secx#.
#y'=1/secx (secx)'=secxtanx/secx=tanx#1
Length = #int sqrt(1+(y')^2) dx#,
with #y = ln|secx| # and x from #0 to pi/4#
#=int sqrt(1+tan^2x) dx#, for the limits
#=int secx dx#, for the limita
#=[ln(secx+tanx)],# between #x = 0 and pi/4#
#=ln(sec(pi/4)+tan(pi/4))=ln(sqrt2+1)#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the length of the curve ( y = \ln|\sec(x)| ) from ( 0 \leq x \leq \frac{\pi}{4} ), you can use the arc length formula. The arc length formula for a curve ( y = f(x) ) from ( x = a ) to ( x = b ) is given by:

[ L = \int_a^b \sqrt{1 + \left( f'(x) \right)^2} , dx ]

First, find the derivative ( f'(x) ) of ( y = \ln|\sec(x)| ). Then, substitute ( f'(x) ) into the arc length formula and integrate over the given interval ( 0 \leq x \leq \frac{\pi}{4} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7