- #1

joemama69

- 399

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## Homework Statement

P = pi

Evaluate [tex]\int[/tex] F [tex]\cdot[/tex]dr where c is the curve given by r(t) = (t+sin[tex]\pi[/tex]t)i + (2tcos[tex]\pi[/tex]t)j

F = (4x

^{3}y

^{2}- 2xy

^{3}) i + (2x

^{4}y - 3x

^{2}y

^{2}+ 4y

^{3})j

## Homework Equations

## The Attempt at a Solution

When I dot them I get an extremely long expression.

[tex]\int[/tex] 4x

^{3}y

^{2}t - 4xy

^{3}t - 2xy

^{3}sinPt + 4x

^{4}yt + 2x

^{4}cosPt - 6x

^{2}y

^{2}t - 3x

^{2}y

^{2}cosPt + 8y

^{3}t + 4y

^{3}cosPt dt evaluated from t = 0 to to = 1

2x

^{3}y

^{2}- 2xy

^{3}+2Pxy

^{3}cosPt + 2x

^{4}y + 2Px

^{4}ysinPt - 3x

^{2}y

^{2}- 3Px

^{2}y

^{2}sinPt + 4y

^{3}+ 4Py

^{3}sinPt