Recent content by rocket

I'm working on a physics problem, and i got stuck on an integral. the entire question is as follows: ---------------------------- Magnetostatics treats the "source current" (the one that sets up the field) and the "recipient current" (the one that experiences the force) so...

i want to prove that this integral along a closed loop: \oint (1/r^2) dr is equal to zero. but I'm not sure how to prove it. i was wondering if someone can show me a rigid proof for this. I think I'm missing something here because I'm not really that familiar with loop integrals.

let f:U \rightarrow R^n be a differentiable function with a differentiable inverse f^{-1}: f(u) \rightarrow R^n . if every closed form on U is exact, show that the same is true for f(U). Hint: if dw=0 and f^{\star}w = d\eta, consider (f^{-1})^{\star}\eta...

let B_n(r) = \{x \epsilon R^n| |x| \le r\} be the sphere around the origin of radius r in R^n. let V_n(r) = \int_{B_n(r)} dV be the volume of B_n(r). a)show that V_n(r) = r^n * V_n(1) b)write B_n(1) as I*J(x) * B_{n-2}(x,y), where I is a fixed interval for the variable x, J an...

let B_n(r) = \{x \epsilon R^n| |x| \le r\} be the sphere around the origin of radius r in R^n. let V_n(r) = \int_{B_n(r)} dV be the volume of B_n(r). a)show that V_n(r) = r^n * V_n(1) b)write B_n(1) as I*J(x) * B_{n-2}(x,y), where I is a fixed interval for the variable x, J an...

closed form?? let f:u \rightarrow R^n be a differentiable function with a differentiable inverse f^{-1}: f(u) \rightarrow R^n . if every closed form on u is exact, show that the same is true for f(u). Hint: if dw=0 and f^{\star}w = d\eta, consider (f^{-1})^{\star}\eta. i don't...

let B_n(r) = \{x \epsilon R^n| |x| \le r\} be the sphere around the origin of radius r in R^n. let V_n(r) = \int_{B_n(r)} dV be the volume of B_n(r). a)show that V_n(r) = r^n * V_n(1) b)write B_n(1) as I*J(x) * B_{n-2}(x,y), where I is a fixed interval for the variable x, J an...

Hi, I'm not sure how to do this question. Any help would be great. Let B be the region in the first quadrant of R^2 bounded by xy=1, xy=3, x^2-y^2=1, x^2-y^2=4. Find \int_B(x^2+y^2) using the substitution u=x^2-y^2, v=xy. . Use the Inverse Function theorem rather than solving for x...