http://www.ck12.org Chapter 7. Integration Techniques
Example 1:
Evaluate∫ 1 ∞dxx.
Solution:
We notice immediately that the integral is an improper integral because the upper limit of integration approaches
infinity. First, replace the infinite upper limit by the finite limitland take the limit oflto approach infinity:
∫∞
1dx
x =llim→∞∫l
1dx
x
=llim→∞[lnx]l 1
=llim→∞(lnl−ln 1)
=llim→∞lnl
=∞.Thus the integral diverges.
Example 2:
Evaluate∫ 2 ∞dxx 2.
Solution:
∫∞
2dx
x^2 =llim→∞∫l
2dx
x^2
=llim→∞[− 1
x]l
2
=llim→∞(− 1
l +1
2
)
=^12.
Thus the integration converges to^12.
Example 3:
Evaluate∫+−∞∞ 1 +dxx 2.