Q. 30

Evaluate the following definite Integrals:


Answer :

For this we have to apply integration by parts


Let u and v be two functions then



To choose the first function u we use “ILATE” rule


That is


I=inverse trigonometric function


L=logarithmic function


A=algebraic function


T=trigonometric functions


E=exponential function


So in this preference, the first function is chosen to make the integration simpler.


Now, In the given question x2 is an algebraic function and it is chosen as u(A comes first in “ILATE” rule)


So first let us integrate the equation and then let us substitute the limits in it.


Note that and











Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration FormulaFundamental Integration FormulaFundamental Integration Formula59 mins
Interactive Quiz on Integration by SubstitutionInteractive Quiz on Integration by SubstitutionInteractive Quiz on Integration by Substitution47 mins
Lecture on Integration by partsLecture on Integration by partsLecture on Integration by parts55 mins
Lecture on some forms of integrationLecture on some forms of integrationLecture on some forms of integration54 mins
Lecture on integration by partial fractionsLecture on integration by partial fractionsLecture on integration by partial fractions62 mins
Interactive Quiz on Integration by PartsInteractive Quiz on Integration by PartsInteractive Quiz on Integration by Parts56 mins
Integration by SubstitutionIntegration by SubstitutionIntegration by Substitution56 mins
Practice Questions on  Definite Integral as Limit of a SumPractice Questions on  Definite Integral as Limit of a SumPractice Questions on Definite Integral as Limit of a Sum47 mins
Definite Integral as Limit of a Sum Means ?Definite Integral as Limit of a Sum Means ?Definite Integral as Limit of a Sum Means ?47 mins
Definite Integration | Ready for a quiz?Definite Integration | Ready for a quiz?Definite Integration | Ready for a quiz?50 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses