# How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=e^-x, y=0, x=0, x=1#, about the x axis?

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

To find the volume of the solid generated by revolving the region bounded by the graphs ( y = e^{-x} ), ( y = 0 ), ( x = 0 ), and ( x = 1 ) about the x-axis, you use the disk method. The volume ( V ) is given by the integral ( V = \pi \int_{a}^{b} (f(x))^2 , dx ), where ( f(x) ) represents the height of the region. In this case, ( f(x) = e^{-x} ). Integrating from ( x = 0 ) to ( x = 1 ) gives ( V = \pi \int_{0}^{1} (e^{-x})^2 , dx ). Solving this integral yields ( V = \pi \int_{0}^{1} e^{-2x} , dx ). Applying the antiderivative and evaluating the limits of integration gives the volume of the solid.

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)=xcos(x-2)# on #x in [1,2]#?
- What is the arc length of #f(x) = x^2e^(3x) # on #x in [ 1,3] #?
- Show that # xsin2x # is a solution to the DE # y'' + 4y = 4cos2x #?
- How do you solve the differential #dy/dx=(x+1)/(x^2+2x-3)^2#?
- How do you find the volume of the region left of #y = sqrt(2x)# and below #y = 2# rotated about the y-axis?

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