You are watching: Evaluate the line integral, where c is the given curve.
How do you solve this by using the following parametrics? I split them up but got a negative answer of -1/3. What"s wrong?
For $C_1$ got, $\langle t, t/2\rangle$, $0 \leq t \leq 2$.
For $C_2$ got, $\langle t, 3-y\rangle$, $2 \leq t \leq 3$.

Hints:
$$\;\;\;(0,0)\to(2,1)\,:\;\;\; 0\le x\le 2\;,\;\;y=\frac x2\implies$$
$$\int\limits_{(0,0)}^{(2,1)}(x+2y)dx+x^2dy=\int\limits_0^2 (x+x)dx+x^2\left(\frac12\,dx\right)=\int\limits_0^2\left(\frac12x^2+2x\right)dx=$$
$$=\frac16\cdot8+4=\frac{16}3$$
and something similar with the other one...
See more: How Far Is Seguin From San Antonio, Tx To Seguin, Tx, Distance From San Antonio, Tx To Seguin, Tx
Added:
$$(2,1)\to(3,0):\;\;\;2\le x\le 3\;,\;\;y=-x+3\implies$$
$$\int\limits_{(2,1)}^{(3,0}(x+2y)dx+x^2dy=\int\limits_2^3 (x+2(-x+3))dx+x^2\left((-1)\,dx\right)=\int\limits_2^3\left(-x^2-x+6\right)dx=$$
$$\left.-\frac13x^3\right|_2^3-\left.\left.\frac12x^2\right|_2^3+6x\right|_2^3=-\frac{19}3-\frac52+6=-\frac{17}6$$
Share
Cite
Follow
edited Apr 30 "13 at 21:05
answered Apr 30 "13 at 20:56

DonAntonioDonAntonio
203k1717 gold badges116116 silver badges269269 bronze badges
$\endgroup$
2
Add a comment |
1
$\begingroup$
Try writing these integrals as$$\int_C (x+2y,x^2)\cdot (dx,dy)$$where $\cdot$ is the usual inner product.Now, for $C_1$, make $(x,y)=(x(t),y(t))=(t,\frac{t}{2})$ (if your parametrization is correct), from which we have $dx=dt$ and $dy=\frac{dt}{2}$. You can now easily integrate with respect to $t$, within the range where $t$ varies.
Share
Cite
Follow
answered Apr 30 "13 at 20:50

MarraMarra
4,4941919 silver badges5454 bronze badges
$\endgroup$
Add a comment |
Not the answer you're looking for? Browse other questions tagged multivariable-calculus or ask your own question.
Featured on Meta
Linked
0
How do you evaluate this line integral, where C is the given curve?
Related
0
How do you evaluate this line integral, where C is the given curve?
1
Evaluate the line integral $\int_C \ x^2 dx+(x+y)dy \ $
1
Evaluate a line integral using the fundamental theorem of line integrals
1
Evaluate the line integral given the path of a helix?
0
Evaluate the line integral given the pathway C= C1+ C2
1
Evaluate line integral without Green's Theorem
0
Evaluate integral where $C$ is the path of straight line segments in 3D
Hot Network Questions more hot questions

ugandan-news.comematics
Company
Stack Exchange Network
site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.10.19.40496
ugandan-news.comematics Stack Exchange works best with JavaScript enabled

Your privacy
By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.