Question

Show that the differential form in the integral is exact. Then evaluate the integral. (0.4.4) sin y cosx dx + cos y sin x dy + 4 dz (1,0,0) s Compute the partial derivatives. ӘР ON ay dz Compute the partial derivatives. OM ap dz Compute the partial derivatives. ON OM ду Select the correct choice below and fill in any answer boxes within your choice. O A sin y cos x dx + cos y sin x dy + 4 dz = - (Type an exact answer) B. The differential form is not exact

Answer 1

AT Page 1 Dule : Ersl. Given integscal is ftp cha) + سلام an an ay $0,4,42 Sinycosxdat.cony Sinxdy 4:402 ☺ > M2.Stay conx, N = Cosy Sinx-_-_PEL Now dl=0 ON 20 of - ON dy Oz og az OM LO al o om al az -az. an IN - Cosycoss om - cosycare => en adM 7 given differential form is exact put Siny Corse du + Cosy linn dy +4dz = df - for some of and integral value is Hook $40,44)-$410,0) * we find of by integrating the equation Cosy sinn, at = 4 dy fup to a comstant f(x,y,z) - Sing Sinx + g (Y, Z) 6 es Scanned with So we at Sinycoste of ax - az from eq 3 16 CarScanner

Page 1 Dute: Page 3 from egr * (044) zont hpxois hoos txp xoay toros = $(0,4,4) = f(1,0,0) (sin(4) Sin@) +4642+c] - [Sincos Sin Cu +410)+c] = 16+ c C = 16 Any es Scanned with CamScanner