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

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

Grade:12

5 Answers

Parvez ali
askIITians Faculty 47 Points
9 years ago

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Parvez Ali
askIITians Faculty

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
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

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
9 years ago
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

SADDAM NAFEES
26 Points
9 years ago

0
Thanks & Regards
saddam nafees,
askIITians Faculty
SEKHAR
20 Points
9 years ago
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.

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