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Midterm

MATH 2B Midterm: MATH2B, Chapter 5.2 term test 1Premium


Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Midterm

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x dx
b
a
32
Solving for integral example
x Δ = n
ba= 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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