# What is the arc length of #f(x)=-xsinx+xcos(x-pi/2) # on #x in [0,(pi)/4]#?

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

To find the arc length of the function ( f(x) = -x\sin(x) + x\cos(x - \frac{\pi}{2}) ) on the interval ( x ) in ( [0, \frac{\pi}{4}] ), we can use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{{dy}}{{dx}}\right)^2} , dx ]

First, find the derivative of ( f(x) ):

[ f'(x) = -\sin(x) - x\cos(x) + \cos(x - \frac{\pi}{2}) + x\sin(x - \frac{\pi}{2}) ]

Then, calculate the square of the derivative:

[ [f'(x)]^2 = (-\sin(x) - x\cos(x) + \cos(x - \frac{\pi}{2}) + x\sin(x - \frac{\pi}{2}))^2 ]

Next, integrate ( \sqrt{1 + [f'(x)]^2} ) over the interval ( [0, \frac{\pi}{4}] ):

[ L = \int_{0}^{\frac{\pi}{4}} \sqrt{1 + [f'(x)]^2} , dx ]

Finally, evaluate the integral to find 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.

- What is the arclength of #f(x)=(x-3)e^x-xln(x/2)# on #x in [2,3]#?
- How do you find the volume of the solid generated by revolving the region bounded by the curves y = 1/x, y = x^2, x = 0, and y = 2 rotated about the x-axis?
- Is there a systematic way to determine an integrating factor #mu(x,y)# of the form #x^n y^m#, given a not-necessarily-exact differential equation?
- How mush work is done in lifting a 40 kilogram weight to a height of 1.5 meters?
- How do you draw the slope field of the differential equation #dy/dx=1/3(y-1)^(1/3)# ?

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