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`A_(1) -= y = x^(2) -1` <br> `A_(2) -= y = 1` <br> Curve is <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T6_MAT_C19_SLV_005_S01.png" width="80%"><br> Required area = area of ABCA <br> `= underset(-sqrt2) overset(sqrt2)(int) (1-x^(2) +1) dx` <br> `= 2 underset(0)overset(sqrt2)(int) (2-x^(2))` dx <br> `= 2(2x - (x^(3))/(3))_(0)^(sqrt2)` <br> `= 2 ( 2sqrt2 - (2sqrt2)/(3))` sq. unit <br> `= (8sqrt2)/(3)` sq. unit **Area as a definite integral**

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**Examples: Find the area of the region bounded by the curve `y^2 = 2y - x` and the y-axis.**

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