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# Evaluate the line integral.$\int_{C} 2 y d s,$ where $C$ is the portion of $y=x^{2}$ from (0,0) to (2, 4), followed by the line segment to (3,0)

## $\approx 16.9424+4 \sqrt{17} \approx 33.4348$

Vectors

Vector Calculus

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##### Lily A.

Johns Hopkins University

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Missouri State University

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University of Nottingham

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Idaho State University

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### Video Transcript

given a go to my ideas, this sea is presenting bicycle two x squared from zero Bama zero core Bless the lines. That bill from to come up or through \$3 a musical will be something right going from here and then coming back here. So? So my ex one is a good day. Bye. One will be equal to the square. The Yes, Mandel Big will do the dairy with theirs off board into d d. Violent. So this is a girl to one square plus the woody who's squared. Really one. So this equals one plus 40 square D d one. My ex to will they will do to plus three minus two in duty is it will do to Les De then my by two is it will do full blurs. Zero minus Would into a deal was four minus four b there. Oh, my ideas to will be equal to X dash One more square plus minus Four walls were linking to. It was rude off 17 d d to therefore my cough. See the word? Yes, the big will do. Zero do four. Do we do the's Square? Underwood one minus. Woody's where the one plus 4 to 02 and do four minus were key crude 17 dd two. So this is a full toe to win toe one minus 40 square. Say is equal to you. I get the Esquire's ago to U minus one by 4 to 0 to four U minus one, but over into U to the power half into the U plus four Blue Zino, you're 17 outside. Four minus will be DD two. So this is a will do do 0 to 4 U to the power three by two Divided where were minor U to the power half divided by four. Do you less or does you know the road 17 Well minus school. Be deep, too. This is a wilder integration. This is you to depowered by going to before minus you to dip our tree by do before integration going from 0 to 4. Bless do Route 17 would be minus. You will d squared Or do you put the values we will get to been to 32 by four minus stayed by four plus two Road seven being minus 16 plus. So this is equal to seven plus 32 Road 17

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#### Topics

Vectors

Vector Calculus

##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp