# What is the surface area produced by rotating #f(x)=sinx-cosx, x in [0,pi/4]# around the x-axis?

The surface area due to

the interval of the integral

now let setup the interval of the definite integral to determine the surface area:

show below the surface area revolving (shaded):

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

The surface area produced by rotating ( f(x) = \sin(x) - \cos(x) ) around the x-axis over the interval ([0, \frac{\pi}{4}]) is approximately (2.368) square units.

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

The surface area produced by rotating (f(x) = \sin(x) - \cos(x)) around the x-axis on the interval ([0, \frac{\pi}{4}]) can be calculated using the formula for the surface area of a curve rotated around the x-axis, which is (\int_{a}^{b} 2\pi y \sqrt{1 + (y')^2} , dx), where (y = f(x)) and (y' = \frac{dy}{dx}).

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.

- 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