1936 --> 1936.000
However; I believe your question is wrong.
519/6=86.5
915/7=130.7142
439/7=62.7142
812/9=90.2222
so i think its the 1st on but i may be wrong.
Step-by-step explanation:
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Answer:
92/1125
Step-by-step explanation:
Answer:
![\int\limits^._c {(y+5sinx)} \, dx +(z^{2}+2cosy )dy+x^{3} dz = \pi](https://tex.z-dn.net/?f=%5Cint%5Climits%5E._c%20%7B%28y%2B5sinx%29%7D%20%5C%2C%20dx%20%2B%28z%5E%7B2%7D%2B2cosy%20%29dy%2Bx%5E%7B3%7D%20dz%20%3D%20%5Cpi)
Step-by-step explanation:
The line integral is ![\int\limits^._c {(y+5sinx)} \, dx +(z^{2}+2cosy )dy+x^{3} dz\\ C:r(t)=sint,cost,sin2t, where , 0$\leq$t$\leq$2\pi\\x=sint,y=cost, z=sin2t\\dx=costdt,dy=-sintdt,dz=2cos2tdt\\therefore](https://tex.z-dn.net/?f=%5Cint%5Climits%5E._c%20%7B%28y%2B5sinx%29%7D%20%5C%2C%20dx%20%2B%28z%5E%7B2%7D%2B2cosy%20%29dy%2Bx%5E%7B3%7D%20dz%5C%5C%20C%3Ar%28t%29%3Dsint%2Ccost%2Csin2t%2C%20where%20%2C%200%24%5Cleq%24t%24%5Cleq%242%5Cpi%5C%5Cx%3Dsint%2Cy%3Dcost%2C%20z%3Dsin2t%5C%5Cdx%3Dcostdt%2Cdy%3D-sintdt%2Cdz%3D2cos2tdt%5C%5Ctherefore)
![\int\limits^._c {(y+5sinx)} \, dx +(z^{2}+2cosy )dy+x^{3} dz](https://tex.z-dn.net/?f=%5Cint%5Climits%5E._c%20%7B%28y%2B5sinx%29%7D%20%5C%2C%20dx%20%2B%28z%5E%7B2%7D%2B2cosy%20%29dy%2Bx%5E%7B3%7D%20dz)
![\int\limits^._c {(cost+5sin(sint)} \, costdt +(sin^{2}2t+2cos(cost) ).-sintdt+sin^{3}t(2cos2tdt)\\](https://tex.z-dn.net/?f=%5Cint%5Climits%5E._c%20%7B%28cost%2B5sin%28sint%29%7D%20%5C%2C%20costdt%20%2B%28sin%5E%7B2%7D2t%2B2cos%28cost%29%20%29.-sintdt%2Bsin%5E%7B3%7Dt%282cos2tdt%29%5C%5C)
![$\int_{0}^{2\pi} [{(cos^{2} t+5costsin(sint)} \, -(sintsin^{2}2t+2sintcos(cost) )+2sin^{3}t(cos2t)]dt\\](https://tex.z-dn.net/?f=%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%20%5B%7B%28cos%5E%7B2%7D%20t%2B5costsin%28sint%29%7D%20%5C%2C%20-%28sintsin%5E%7B2%7D2t%2B2sintcos%28cost%29%20%29%2B2sin%5E%7B3%7Dt%28cos2t%29%5Ddt%5C%5C)
Now evaluate the integrals separately
![=$\int_{0}^{2\pi} cos^2t dt$ =$\int_{0}^{2\pi}\frac{1+cos2t}{2}dt=\frac{1}{2}$\int_{0}^{2\pi}(1+cos2t)dt](https://tex.z-dn.net/?f=%3D%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%20cos%5E2t%20dt%24%20%3D%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5Cfrac%7B1%2Bcos2t%7D%7B2%7Ddt%3D%5Cfrac%7B1%7D%7B2%7D%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%281%2Bcos2t%29dt)
![=\frac{1}{2}[t+\frac{1}{2}sin2t] =\frac{1}{2}2\pi=\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%5Bt%2B%5Cfrac%7B1%7D%7B2%7Dsin2t%5D%20%3D%5Cfrac%7B1%7D%7B2%7D2%5Cpi%3D%5Cpi)
![$\int_{0}^{2\pi}5costsin(sint)dt=0\\](https://tex.z-dn.net/?f=%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D5costsin%28sint%29dt%3D0%5C%5C)
![$\int_{0}^{2\pi}sintsin^{2}2tdt](https://tex.z-dn.net/?f=%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7Dsintsin%5E%7B2%7D2tdt)
![=$\int_{0}^{2\pi}sint(2sintcost)^{2}dt](https://tex.z-dn.net/?f=%3D%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7Dsint%282sintcost%29%5E%7B2%7Ddt)
![4$\int_{0}^{2\pi}sin^{3}tcos^{2}tdt = 0 ,by,maple](https://tex.z-dn.net/?f=4%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7Dsin%5E%7B3%7Dtcos%5E%7B2%7Dtdt%20%3D%200%20%2Cby%2Cmaple)
![$\int_{0}^{2\pi}2sintcos(cost)dt = 0 ,by,maple](https://tex.z-dn.net/?f=%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D2sintcos%28cost%29dt%20%3D%200%20%2Cby%2Cmaple)
![$\int_{0}^{2\pi}2sin^{3}t(cos2t)dt = 0 ,by,maple](https://tex.z-dn.net/?f=%24%5Cint_%7B0%7D%5E%7B2%5Cpi%7D2sin%5E%7B3%7Dt%28cos2t%29dt%20%3D%200%20%2Cby%2Cmaple)
therefore
![\int\limits^._c {(y+5sinx)} \, dx +(z^{2}+2cosy )dy+x^{3} dz = \pi](https://tex.z-dn.net/?f=%5Cint%5Climits%5E._c%20%7B%28y%2B5sinx%29%7D%20%5C%2C%20dx%20%2B%28z%5E%7B2%7D%2B2cosy%20%29dy%2Bx%5E%7B3%7D%20dz%20%3D%20%5Cpi)