Integrating Definite Integral: 3x^5 + 4x^4 + x^2

Click For Summary
SUMMARY

The discussion focuses on integrating the function (3x^5 + 4x^4 + x^2)/x^3 with limits from 1 to 3. The correct integration yields the result of 3x^2 + 4x + ln(x) after addressing the integration of x^-1, which is ln(x). The participant initially misunderstood the implications of integrating x^-1, thinking it would lead to infinity, but was corrected that the integral is finite when evaluated at the specified limits.

PREREQUISITES
  • Understanding of definite integrals
  • Familiarity with polynomial functions
  • Knowledge of logarithmic functions, specifically ln(x)
  • Basic calculus concepts, including integration techniques
NEXT STEPS
  • Study the properties of definite integrals
  • Learn advanced integration techniques, including integration by parts
  • Explore the applications of logarithmic functions in calculus
  • Practice solving integrals involving rational functions
USEFUL FOR

Students and educators in calculus, mathematicians, and anyone looking to deepen their understanding of integration techniques and logarithmic functions.

noobie!
Messages
57
Reaction score
0
there's a que which baffles me today,so i hope any1 of you could help me to clear my doubt,here is the que:

integrate with limit 3 on top n 1 below (3x^5 + 4x^4 + x^2)/x^3 dx ..
so here goes my sol please rectify me..
SOL: 3x^2 + 4x + x^-1
then integrate it
x^3 + 2x^2..<<<<then what about x^-1 ?if we integrate it the denominator will become infinite so any value + infinity it will become infinity?am i wright?pl help me,thanks a lot...
 
Physics news on Phys.org
The integral of x^-1 is ln(x)... taken at the limits given, that's not infinity. You're method for solving is sound, but x^-1 is just one that you have to memorize.
 
Dr. Lady said:
The integral of x^-1 is ln(x)... taken at the limits given, that's not infinity. You're method for solving is sound, but x^-1 is just one that you have to memorize.

thanks a lot,i didnt thought of that..thanks...:smile:
 

Similar threads

Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Result of this integral in large Lambda limit
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Definite integral is undefined and not undefined
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Integration with different infinitesimal intervals
  • · Replies 31 ·
2
Replies
31
Views
5K
High School Why is this definite integral a single number?
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Express the limit as a definite integral
  • · Replies 16 ·
Replies
16
Views
4K
MHB What is the Slant Asymptote of $\dfrac{4x^3-10x^2-11x-1}{x^2-3x}$?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How Do You Integrate Expressions Like These?
  • · Replies 6 ·
Replies
6
Views
2K