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`(8)/(3)` sq units `(4)/(3)` sq units `(9)/(4)` sq units`(7)/(3)` sq units

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ASolution :

Given curves are <br> `y^(2)=x+1" ... (i)"` <br> `y^(2)=-x+1" ... (ii)"` <br> curve (i) is the parabola having axis y = 0and vertex (-1, 0). <br> Curve (ii) is the parabola having axis y = 0 and vertex (1, 0). <br> On solving Eq. (i) from Eq. (ii), we get 2x = 0 implies x = 0 <br> From Eq. (i), x = 0 implies `y = pm 1` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_EGN_PRG_MAT_C23_E01_043_S01.png" width="80%"> <br> Required area <br> `=int_(-1)^(1)(x_(1)-x_(2))dy` <br> `=int_(-1)^(1)[(1-y^(2))-(y^(2)-1)]dy=2int_(-1)^(1)(1-y^(2))dy` <br> `=2[y-(y^(3))/(3)]_(-1)^(1)` <br> `=2[(1-(1)/(3))-(-1+(1)/(3))]=(8)/(3)` sq unit