Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows page 1. to view the full**4 pages of the document.**●x dx

∫

b

a

32

○Solving for integral example

○x Δ = n

b−a= n

b

■Solve for xΔ

○0 kxk= + n

b=n

kb

■Solve for x

k

○(x) fk= n2

3b(k)

2 2

■Solve for f(x) k

○( )( )lim

n→∞ ∑

n

k=1 n2

3b k

2 2

n

b

●Compile the limit with the given information

○n3

3b3lim

n→∞ ∑

n

k=1

k2

●Move constants out to deal with only k2

○( )lim

n→∞ n2

3b3

6

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

●is replaced by∑

n

k=1

k2)( 6

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

○( )lim

n→∞ 2n2

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

3

■Simplify by cancelling out terms

○( )lim

n→∞ 2n2

b2n

32

■Simplify

○b3

Fundamental Theorem of Calculus #1

●If ,(x) (t)dtf = ∫

x

a

g (x) g(x)f′=

●Ex

○(x) n(1 )dtF = ∫

x

a

l+t2

■ is the integral of on the interval (x)F n(1 )l+t2a,x][

Fundamental Theorem of Calculus

Section 5.3

Integral

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