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Grade: 12

                        

Find the area bounded by the curves y = x|x| , x - axis , x = 1 & x = -1.

6 years ago

Answers : (5)

Parvez ali
askIITians Faculty
47 Points
							
147-489_140303-104425.jpg



Thanks & Regards
Parvez Ali
askIITians Faculty

6 years ago
Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							y=x^2  for x>0
y=-x^2 for x<0


if we are just checking the magnitude of area,


Sher Mohammad,
B.tech, IIT Delhi

6 years ago
bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							Area bounded :
Integral ofy = x|x| , limits -1 to 1
It should be divided in two parts , -1 to 0 and 0 to 1
Integral 1= -x^2 , -1 to 0 = 1/3
Integral 2= x^2 , 0 to 1 = 1/3
Total area bounded : 2/3 sq. units
Thanks & Regards
Bharat Bajaj
askIITians Faculty
IIT Delhi

6 years ago
SADDAM NAFEES
26 Points
							
0
Thanks & Regards
saddam nafees,
askIITians Faculty
6 years ago
SEKHAR
20 Points
							x|x| has "-" sign in (-1,0) and "+" sign in (1,0) 
Therefore, to get area of the curve x|x| integrate the function 
i.e., as -x^2 at (-1,0) and x^2 at (1,0)
integrating the above two functions we get 
*  integration of -x^2 at (-1,0) is -1/3 (and)
*  integration of x^2 at (1,0) is also -1/3
Therefore, adding the above two we get -2/3, Since the area cannot be negative, we take its modulus and it becomes 2/3.
Hence, the area of the Curve  x|x| is "2/3" from x=1 to x=-1.
						
6 years ago
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