Given, R={(x,y):5x2≤y≤2x2+9} Here, we have two curves y=5x2 and y=2x2+9, point of intersection of both curves is find by solving both equations i.e. 5x2‌‌=2x2+9 ⇒‌‌x2‌‌=3⇒x=±√3
∴‌‌‌ Area ‌‌‌=
∫
−√3
√3(2x2+9−5x2)dx ‌‌=2‌
∫
0
√3(9−3x2)dx ‌‌=2[9x−x3]0√3 ‌‌=2[9√3−3√3] ‌‌=12√3‌ sq units ‌