Q. 394.0( 2 Votes )

Evaluate the following integrals:

Answer :

Let x = cos t ; t = cos - 1x

dx = - sin t dt

We know that sin 2t = 2 sint×cost

We have

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking first function to the one which comes first in the list.

Here t is first function and sin 2t as second function.

We know that cos2t = 2cos2t - 1 and sin2t = 2sint×cost and sint = √1 - cos2t

Replacing in above equation

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 FormulaFREE Class
Lecture on some forms of integration54 mins
Lecture on Integration by parts55 mins
Integration by Substitution56 mins
Interactive Quiz on Integration by Substitution47 mins
Definite Integration | Ready for a quiz?FREE Class
Lecture on integration by partial fractions62 mins
Interactive Quiz on Integration by PartsFREE Class
Microsporogenesis & Megasporogenesis49 mins
Meselson and Stahl experiment49 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
view all courses