2
answers
0
watching
14
views
17 Nov 2019
Let nabla f = -6xe^-x^2 sin (5y) i + 15e^-x^2 cos(5y) j. Find the change in f between (0, 0) and (1, pi/2) in two ways. (a) First, find the change by computing the line integral integral_c nabla f middot dr, where C is a curve connecting (0, 0) and (1, pi 2). The simplest curve is the line segment joining these points. Parameterize it: with 0 lessthanorequalto t lessthanorequalto 1, r(t) = t i+ (pi/2)t j So that integral_c nabla f middot dr = integral^1_0 -6te^(-t^2)sin((5pi/2)t) + 15e^(-t^2)cos((5 pi/2)t)(pi. dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily find a numerical estimate for it. It's easier to find integral_c nabla f middot dr as the sum integral_C_1 nabla f middot dr + integral_c_2 nabla f middot dr, where C_1 is the line segment from (0, 0) to (1, 0) and C_2 is the line segment from (1, 0) to (1, pi/2). Calculate these integrals to find the change in f. integral_C_1 nabla f middot dr = integral_C_2 nabla f middot dr = 0.150811 So that the change in f = integral_c nabla f middot r = integral_c_1 nabla f middot dr + integral_c_2 nabla f middot dr. = (b) By computing values of f. To do this, First find f(x, y) = Thus f(0, 0) = and f(1, pi/2) = and the change in f is
Let nabla f = -6xe^-x^2 sin (5y) i + 15e^-x^2 cos(5y) j. Find the change in f between (0, 0) and (1, pi/2) in two ways. (a) First, find the change by computing the line integral integral_c nabla f middot dr, where C is a curve connecting (0, 0) and (1, pi 2). The simplest curve is the line segment joining these points. Parameterize it: with 0 lessthanorequalto t lessthanorequalto 1, r(t) = t i+ (pi/2)t j So that integral_c nabla f middot dr = integral^1_0 -6te^(-t^2)sin((5pi/2)t) + 15e^(-t^2)cos((5 pi/2)t)(pi. dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily find a numerical estimate for it. It's easier to find integral_c nabla f middot dr as the sum integral_C_1 nabla f middot dr + integral_c_2 nabla f middot dr, where C_1 is the line segment from (0, 0) to (1, 0) and C_2 is the line segment from (1, 0) to (1, pi/2). Calculate these integrals to find the change in f. integral_C_1 nabla f middot dr = integral_C_2 nabla f middot dr = 0.150811 So that the change in f = integral_c nabla f middot r = integral_c_1 nabla f middot dr + integral_c_2 nabla f middot dr. = (b) By computing values of f. To do this, First find f(x, y) = Thus f(0, 0) = and f(1, pi/2) = and the change in f is
anutaa666Lv2
5 Jan 2023
Unlock all answers
Get 1 free homework help answer.
Already have an account? Log in
Jamar FerryLv2
20 Jun 2019
Get unlimited access
Already have an account? Log in