## Vineet Loomba is teaching live on Unacademy Plus

APPLICATIONS OF INTEGRALS (AREA UNDER CURVES) JEE MAIN AND ADVANCED IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 Doubts/Feedback in Comment Section * Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates or search me on Google * Share among your peers as SHARING is CARING!!

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. Find the area bounded by the curves {(x, y) : y 2 x, y The curves intersect each other at x = 0 and x = 1 as shown in figure. The points of intersection are (-1, 1), (0, 0) and (1, 1) N) Sol. Since, the region is symmetric about y-axis, the required area is 2[area of region OABO] Hence, units? MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Find the area ofthe region {(x,y): *-x-1sys-i) Sol: Let the given region be = {(x, y) : x"-x Consider the curves v--x-1 1-5 1+N5 and y- The curves (1) & (2) intersect at the points x for which y <-1 "Region R Fig 4.26 yzx-x-1 represents the region inside the parabola (1) including the curve y s-1 represents the region below the line yncluding the line A rough sketch of the region R is shown in the figure MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) It is bounded between x=0 and x=1 L 2 3 L-6 sq units. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) |x and y = x2 Find the area enclosed between the curves y Sol: Given equations are y = X2-2 Considerx>0 Solving y = x2-2 and y-x x2-x-2=0 x+1) (x-2) 0 -22f0,-2) x=2 x=2( x > 0) MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Consider x < 0, Solving y = x2-2, y =-X x2 + x-2-0 (X +2) (x + 1)=0 x= 2 or 1 .:. Required area jl-x-(2 -2)] dx >[x-(-2) dr 16 20 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Enroll 934 ENROL for this Course (Free) Recommend Lessons (Like) E Rate and Review the Course ** 15 68 153 ratings - 30 reviews .Comments . Sharing with friends Share MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)