Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**3 pages of the document.**●Shortened: (x)dx

∫

b

a

f

Examples

●x 2 dx

∫

3

1

2 −

○You can either take the area after graphing it out, or take the antiderivative

(integral) directly

○ 2xx2−

■The antiderivative

○3) 2(3) 3( 2− =

■Plug in for b x

○1) 2(1) ( 2− = − 1

■Plug in for a x

○3) − ) 4( − ( 1 =

■Subtract from to find the area between the two pointsa b

The Integral using limit definition

●(x)dx (x)Δx

∫

b

a

f= lim

n→∞ ∑

n

k = 1

fk

●∑

n

k=1

1 = n

●∑

n

k=1

k=2

n(n+1)

●∑

n

k=1

k2=6

n(n+1)(2n+1)

●∑

n

k=1

k3=4

n(n+1)

22

These are a few of the definition used, but there is no need to memorize them.

Definite Integral

Section 5.2

Find area of y = f(x) between a ≤ x ≤ b

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