Calculus help!

posted by .

f(x)=e^x for 0<x<2. Imagine that you have graphed this function in the x-y plane. For each value of x in the domain, erect a square above the curve perpendicular to the x-axis and parallel to the y-z plane where one side runs from the x-axis to the curve. So the square at x=.9 has vertices (.9,0,0), (.9,e^.9,0), (.9,e^.9,e^.9), (.9,0,e^.9). All of these squares together create a volume. Set up an integral to compute the volume exactly.

  • Calculus help! -

    length of side of square = e^x
    area of square = (e^x)^2 = e^2x
    volume = integral dx e^2x from x = 0 to x = 2

    = (1/2)e^2x at x = 2 - at x = 0

    = (1/2)e^4 -(1/2)(1)
    = (1/2)(e^4 -1)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. CALC -- integrals!

    2. f(x)=e^x for 0<x<2. Imagine that you have graphed this function in the x-y plane. For each value of x in the domain, erect a square above the curve perpendicular to the x-axis and parallel to the y-z plane where one side runs …
  2. physics

    You push a 320 N trunk up a 20.0° inclined plane at a constant velocity by exerting a 213 N force parallel to the plane's surface. (a) What is the component of the trunk's weight parallel to the plane?
  3. Physics

    A square, 0.52 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. This axis is perpendicular to the plane of the square. A force of 15.0 N lies in this plane and is applied to …
  4. physics

    A square, 0.52 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. This axis is perpendicular to the plane of the square. A force of 15.0 N lies in this plane and is applied to …
  5. Help!!!

    An electric field of intensity 4.27 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if the following conditions are true. (a) The plane is parallel to the yz-plane. …
  6. physics!!!

    An electric field of intensity 4.27 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if the following conditions are true. (a) The plane is parallel to the yz-plane. …
  7. physical

    An electric field with a magnitude of 3.50 kN/C is applied along the x axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.7 m long assuming that (a) the plane is parallel to the yz plane; (b) the plane …
  8. Biology

    In conventional human radiological imaging (e.g., MRI, PET, CT) of the head, the axial plane is synonymous with the horizontal plane. Which of the following statements about this plane is most accurate?
  9. Engg Mechanics

    Blocks A and B of weight 200N and 100N respectively, rest on a 30 inclined plane and are attached to the post which is held perpendicular to the plane by force P, parallel to the plane, as shown in fig. Assume that all surfaces are …
  10. Engg Mechanics

    Blocks A and B of weight 200N and 100N respectively, rest on a 30 inclined plane and are attached to the post which is held perpendicular to the plane by force P, parallel to the plane, Assume that all surfaces are smooth and that …

More Similar Questions