Question
Mathematics Question on applications of integrals
Area of the region bounded by two parabolas y=x2 and x=y2 is
A
31
B
3
C
41
D
4
Answer
31
Explanation
Solution
The intersection point of parabolas y=x2 and x=y2 is y=(y2)2 ⇒y=y4 ⇒y=0,y=1 ⇒x=0,x=1 So, the intersection point in O(0,0) and (1,1). ∴ Required area =\int_\limits{0}^{1}\left(y_{2}-y_{1}\right) d x =\int_\limits{0}^{1}\left(\sqrt{x}-x^{2}\right) d x =[3/2x3/2−3x3]01=[32x3/2−3x3]01 =[32(1)−31(1)+0−0] =[32−31]=31 We know that, if parabolas are y2=4ax and x2=4by, then area of bounded region is 34a⋅4b. ∴ Required area =31×1=31