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Evaluate the line integral of F(x,y)=(xy) i - (7x^2y) j, where C is given by r(t)= (t^2) i + (t) j, for 0<t<1
possible answers to choose from....
a. 1/15
b. -1/10
c. -4/15
d. -13/30
e. -3/5
f. -23/30
g. -14/15
h. none of these
2 Answers
- 1 decade agoFavorite Answer
r(t)=<t^2, t>
F(x,y)=<xy, -7yx^2>
So
F(r(t))=<t^3,-7t^5>
r'(t)=<2t,1>
We find the dot product of F(r(t)) and r't()
F(r(t)) dot r'(t)=
2t^4-7t^5
Now we integrate that from 0 to 1 and get
(2/5)t^5-(7/6)t^6
Now we use the fundamental theorem of calculus to solve:
Answer: 2/5 -7/6=12/30-35/30= -23/30
Choice F.
- santmann2002Lv 71 decade ago
y=t x=t^2
F(x,y) on C is t^3i-7t^5j
dr= (2ti+j)dt
IntF*dr =Int (2t^4-7t^5)dt (0,1) = 2/5-7/6 = -23/30 (f)
