## 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) Using Entegnation tFind Aeas Under rves CONCEPT O Complete Aea Akea bounded e uve wifh x-axis NOTE :-Aktas above -axis ate Positive. Area bela., -acis (omes out to he negative meke hem posiHve UAe modulus tr a. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example Findl the aua bounded bu the ewve x 5x+6 So1 )L = 2 and 3 Re. Ae 3 5 6 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration The area bounded by the curve : y = 4-x, X-axis and Y-axis 32 (D) None of these SOLUTION: (B) Trace the curve y ,4-x Using step 1 to 3, we can draw the rough sketch of Put y 0 in the given curve to getx-4 as the point of intersecton with X-axis. Put x-0in the given curve to get y-2 as the point of intersection with Y-axis. For the curve, y =Ja-x,4-x20 In figure, Bounded area = 4 4 2. 16 114-x dx =13(4-xN4_x. = 3 sq. units. curve lies only to the left ofx-4 line As any y is positive, curve is above X-axis. 3. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ilustration: Find the area bounded by the curve y sin2x, x-axis and the lines x and x = 4 t/ 2 3 /4 Solution Required area - sin 2xdx+ sin 2xdx /4 Tt/ 2 /2 3-4 3t/4 cos 2x ) /2 cos 2x 2 /2 2 2 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)