Q. 175.0( 1 Vote )

Evaluate: <span l

Answer :

dx


- x = x( - 1) = x (x – 1) (x + 1)


- x > 0 for -1 < x < 0


- x < 0 for 0 < x < 1


- x > 0 for 1 < x < 2


NOTE: Sign is only being considered for the range -1≤ x ≤ 2


dx + dx + dx


dx – dx + dx


I = - +


I =


I =


The required value is .


OR


Let, I = …(1)


Using the property of definite Integral: =


I =


I = …(2)


Adding equation 1 and 2 we get –


2I =


2I =


Putting Cos x = t


-Sin x dx = dt


When x = 0 t = 1


x = t = -1


2I = { }


2I = π


2I = π{tan-1(1) – tan-1(-1)} { tan-1(1) = π/4}


2I = π(π/4 – (-π/4))


I =


Hence,


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Evaluate:<span laMathematics - Board Papers

Evaluate:

Mathematics - Board Papers

Using integrationMathematics - Board Papers

Evaluate:<span laMathematics - Board Papers

Evaluate:<span laMathematics - Board Papers

Evaluate:<span laMathematics - Board Papers