## MathSofiya 3 years ago Evaluate the line integral $\int_c F\cdot dr$ where c is given by $\hat r (t)=t\hat i +sint\hat j +cost \hat k$ $0 \le t le \pi$ and: $\hat r(t)=\hat i +cost \hat j -sint \hat k$ $F(x, y, z)=z\hat i+y \hat j-x\hat k$ x=t y=sint z=cost $\int_0^{\pi}(cost\hat i +sint\hat j-t\hat k)\cdot(\hat i+cos(t) \hat j -sint \hat k)dt$ $\int_0^{\pi}(cost+sintcost+tsint)dt$ $\int_0^{\pi} cost dt+\int_0^{\pi} sintcostdt+\int_0^{\pi}tsintdt$

1. MathSofiya

$sint]_0^{\pi}+\int_0^0 udu+[-tcost+sint]_0^{\pi}$

2. mukushla

mukushla is not typing a reply…whats wrong with site...lol let me check it

3. MathSofiya

LOL...i think mukushla should type a reply

4. mukushla

its allright but what is that middle integral !!?

5. MathSofiya

u substitution u =sint du=cost dt sin(pi)=0 sin(0)=0

6. mukushla

almost done

7. MathSofiya

0?

8. mukushla

yes

9. MathSofiya

cos Pi is -1 though

10. MathSofiya

so negative pi should be the answer?

11. MathSofiya

and cos (0) is 1 oh it cancels out!

12. MathSofiya

no that still doesn't seem right... :(

13. mukushla

i meant 0 for middle integral

14. mukushla

answer is $$\pi$$ ?

15. MathSofiya

the first integral would be zero too and then we have left $[-tcost+sint]_0^{\pi}=\pi$

16. MathSofiya

YAY!

17. mukushla

We are DONE.....;-D