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Chapter 10: Q.0 (page 777)

Read the section and make your own summary of the material.

Short Answer

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The area under a curve, sigma notation and limits of sums can be reviewed

Step by step solution

01

Step 1. Summary

  • Sigma Notation and Properties of sum.
  • Limits of sum, and definition of definite integral.

A study of the accumulation function.

  • The accumulation function A(x) gives the accumulation of area between the horizontal axis and the graph f(x) between 0 to x.

A(x)=鈭�0x鈥�f(x)dx

02

Step 2. Continue

  • Sigma Notation and Properties of sum.

鈭�k=starting_valueending_value鈥�(function_of_k)1.鈭�k=1n鈥�ak+bk=鈭�k=1n鈥�ak+鈭�k=1n鈥�bk2.鈭�k=1n鈥�ak=鈭�k=1p鈭�1鈥�ak+鈭�k=pn鈥�ak

  • Calculating sums of areas of small rectangles using definite integral.

鈭�0x鈥�f(x)dx=limn鈫�鈭�鈥�鈭�k=1n鈥�fck螖x螖x=b鈭�anck=a+k螖x

Thus, the area under a curve, sigma notation and limits of sums can be reviewed.

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Most popular questions from this chapter

Use the definition of the derivative to find f'for each function fin Exercises 39-54

f(x)=2x+1

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649595165778" u=1,-2andv=-3,6

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

v脳wandw脳v

Find a vector in the direction of 8,-7,2and with magnitude 2.

If u and v are nonzero vectors in 鈩�3, what is the geometric relationship between u,v and u脳v?
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