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Find the area bounded by the curves y = x|x| , x - axis , x = 1 & x = -1.
Thanks & RegardsParvez AliaskIITians Faculty
y=x^2 for x>0y=-x^2 for x<0if we are just checking the magnitude of area,Sher Mohammad,B.tech, IIT Delhi
Area bounded :Integral ofy = x|x| , limits -1 to 1It should be divided in two parts , -1 to 0 and 0 to 1Integral 1= -x^2 , -1 to 0 = 1/3Integral 2= x^2 , 0 to 1 = 1/3Total area bounded : 2/3 sq. unitsThanks & RegardsBharat BajajaskIITians FacultyIIT Delhi
0 Thanks & Regards saddam nafees, askIITians Faculty
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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