How do I find the arc length of the curve #y=ln(cos(x))# over the interval #[0,π/4]#?
This integral has to be done using this substitution (parametric formulae):
So:
The integral becomes:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the arc length of the curve y = ln(cos(x)) over the interval [0, π/4], you can use the arc length formula:
Arc Length = ∫[a,b] √(1 + (dy/dx)^2) dx
In this case, the interval is [0, π/4], and the function is y = ln(cos(x)). You'll need to find the derivative dy/dx and then plug into the formula to calculate the arc length.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
- How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region # y = x^3#, #y = 0#, #x = 2# rotated about the y axis?
- What is a solution to the differential equation #dy/dx=(x^2+2)/(4y^3)#?
- Find the length of the curve defined by #y=18(4x^2−2ln(x)), x in[4,6]#?
- How do you solve the differential equation #(dy)/dx=e^(y-x)sec(y)(1+x^2)#, where #y(0)=0# ?
- Let R be the region enclosed by #y= e^(2x), y=0, and y=2#. What is the volume of the solid produced by revolving R around the x-axis?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7