Let ∇=−−x2sin(⃗ +−x2cos(⃗ . find the change in between (0,0) and (/2) in two ways. (a) first, find the change by computing the line integral ∫∇⋅⃗ , where is a curve connecting (0,0) and (/2). the simplest curve is the line segment joining these points. parameterize it: with 0≤≤1, ⃗ = t ⃗ + pi/2*t ⃗ so that ∫∇⋅⃗ =∫10 (-2te^(-t^2)sin(3pi/2*t)+3e^(-t^2)c os(3pi/2*t))*sqrt(1+pi^2/4) 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 ∫∇⋅⃗ as the sum ∫∇⋅⃗ +∫∇⋅⃗ , where is the line segment from (0,0) to (1,0) and is the line segment from (1,0) to (/2). calculate these integrals to find the change in ∫∇⋅⃗ = 0 ∫∇⋅⃗ = so that the change in =∫∇⋅⃗ =∫∇⋅⃗ +∫∇⋅⃗ = e^-1 (b) by computing values of to do this, first find ,y)= thus ,0)= 0 and /2)= , and the change in is e^-1 .