calculus

posted by .

evaluate the double integral
∫R∫ lny/x dA
for the region R is the rectangle defined by 1<x<e^2 and 1<y<e

  • calculus -

    ∫[1,e^2]∫[1,e] lny/x dy dx
    = ∫[1,e^2](y/x (lny - 1))[1,e] dx
    = ∫[1,e^2] [(e/x (1-1))-(1/x (0-1))] dx
    = ∫[1,e^2] 1/x dx
    = lnx [1,e^2]
    = 2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Evaluate the triple integral ∫∫∫_E (x)dV where E is the solid bounded by the paraboloid x=10y^2+10z^2 and x=10
  2. Calculus

    Evaluate the triple integral ∫∫∫_E (x+y)dV where E is bounded by the parabolic cylinder y=5x^2 and the planes z=9x, y=20x and z=0.
  3. Calculus

    Evaluate the triple integral ∫∫∫_E (xy)dV where E is the solid tetrahedon with vertices (0,0,0), (4,0,0), (0,1,0), (0,0,4)
  4. Calculus

    Evaluate the triple integral ∫∫∫_E (z)dV where E is the solid bounded by the cylinder y^2+z^2=1225 and the planes x=0, y=7x and z=0 in the first octant.
  5. Calculus

    Evaluate the triple integral ∫∫∫_E (xyz)dV where E is the solid: 0<=z<=5, 0<=y<=z, 0<=x<=y.
  6. calculus

    Suppose R is the rectangle 1<=x<=4, |y|<=2 and evaluate the double integral ∫R∫f(x,y)dA, where f(x,y)= y/(1+3x^4)^(1/2). I first decided to integrate with respect to y first (which I think I can choose to do) I …
  7. calculus

    evaluate the double integral ∫R∫ ye^x^3 dA for the region R is bounded by x=y/2, x=1, and y=0
  8. Calculus

    Evaluate the following definite integral: integral at a = -1, b=2 -4dx/(9x^2+30x+25) Would I have to separate them in 3 terms as: -4 ∫1/9x^2 + ∫1/30x + ∫1/25 resulting in: -4/(3x^3)+ (15x^2)+ C?
  9. Calculus III

    Use symmetry to evaluate the double integral ∫∫R(10+x^2⋅y^5) dA, R=[0, 6]×[−4, 4]. (Give your answer as an exact number.) ∫∫R(10+x^2⋅y^5) dA=
  10. calculus

    a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i …

More Similar Questions