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Chapter 14: Q. 5 (page 1095)

Calculus of vector-valued functions: Calculate each of the following.

鈭�r(t)dt,wherer(t)=eti+t3j鈭�4k

Short Answer

Expert verified

The value of鈭�r(t)dt=eti+t44j鈭�4tk

Step by step solution

01

Step 1.Given Information

Calculus of vector-valued functions: Calculate each of the following.

鈭�r(t)dt,wherer(t)=eti+t3j鈭�4k

02

Step 2. Now finding the value of ∫r(t)dt

鈭�r(t)dt=鈭�eti+t3j鈭�4kdt鈭�r(t)dt=鈭�etdti+鈭�t3dtj鈭�4鈭�dtk鈭�r(t)dt=eti+t44j鈭�4tk鈭�r(t)dt=eti+t44j鈭�4tk

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Most popular questions from this chapter

Q. Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A smooth surface with a smooth boundary.

(b) A surface that is not smooth, but that has a smooth boundary.

(c) A surface that is smooth, but does not have a smooth boundary

Why is the orientation of S important to the statement of

Stokes鈥� Theorem? What will change if the orientation is

reversed?

Calculus of vector-valued functions: Calculate each of the following.

ddt(r(t)),wherer(t)=3cos2ti+5tj+tt2+1k

UsethevectorfieldF(x,y)=x2eyi+cos(x)sin(y)jandGreen鈥�sTheoremtowritethelineintegralofF(x,y)abouttheunitcircle,traversedcounterclockwise,asadoubleintegral.Donotevaluatetheintegral.

Find the work done by the vector field

F(x,y)=x3y2i+(y-x)j

in moving an object around the triangle with vertices (1,1),(2,2), and (3,1), starting and ending at (2,2).
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