Misc 11 - Chapter 8 Class 12 Application of Integrals

Transcript

Misc 11 Using the method of integration find the area bounded by the curve + =1 [Hint: The required region is bounded by lines + = 1, =1, + =1 and =1 ] We know that = , 0 & , <0 & = , 0 & , <0 So, we can write + =1 as + =1 >0 , >0 + =1 <0 >0 =1 >0 , <0 =1 <0 <0 For + = For + = Hence the figure is Since the Curve symmetrical about & Required Area = 4 Area AOB Area AOB Area ABO = 0 1 where + =1 =1 Therefore, Area ABO = 0 1 1 = 2 2 0 1 =1 1 2 2 0 0 2 2 2 =1 1 2 = 1 2 Hence, Required Area = 4 Area AOB = 4 1 2 = 2 square units