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Lecture 17

MAT136H1 Lecture 17: Improper Integrals pt. 2 & Intro to Arc-LengthPremium


Department
Mathematics
Course Code
MAT136H1
Professor
Anthony Lam
Lecture
17

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MAT136Lecture17ImproperIntegralspt2/IntrotoArcLength
ImproperIntegrals:
Case1: (x)dx
a
f
Case2: ,when(x)dx
b
a
f(a) ± , f(b) ±f= ∞ = ∞
Case3: (x)dx,wherec[a, ]suchthatf(c)
b
a
fb→ ∞
Ex1.
dx
1
ex= lim
b→∞
b
1
ex
 = lim
b→∞ ex
b
1
 
 = lim
b→∞  − eb+e
1
 − = e−∞ +e
1
 =e
1
Ex2.
dxdx
1
0x2
ex
1=  lim
a→∞
1
ax2
ex
1,du dxu =x
1 = 1
x2
du= lim
a→∞
1
a
eu
= lim
a→∞ eu
1
a
= e+ea
1
= lim
a→∞ e+e1
=
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