## Vineet Loomba is teaching live on Unacademy Plus

IIT-JEE VIDEO COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) IIT-JEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITian | IIT-JEE MENtOR Search vineet loomba unacademy" on GOOGLE

REVISION COURSE FOR 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!!

DEFINITE INTEGRATION 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) Properties of Definite Integration lt it The point of this property is to notice that as long as the function and limits are same, the variable of integration that we use in the definite integral won't affect the answer. L REMEMBER I Variable of integration in definite integral is a dummy variable. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dx f(x)dx= -| f(x)dx Example:Evaluate -4x2 + 1 P-2: Solution: dt 2 xV4x1 1/3 1/3 dt dt Sol= 1/2 t 1/2 V4+ 1/2 3 17+1 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 1-2x, X s0 Example: Evaluate fx)dx, where fx)- Solution: f(x)dx=jf(x)dx+ff(x)dx = j(1-2xdx +j(1+2x)dx 1 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Evaluate [x] dx Solution: 2 3 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example Evaluate Solution We note that x3 - x 2 0 on [ 1, 0] and x3 - x S 0 on [0, 1 and that x3--x 2 0 on [1,2]. So by P, we write 0 4 2 2 4 4 2 2 4 4 2 2 4 4 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) /2 Example: Evaluate: log tan x ox 0 Solution: /2 /2 = J (n tan x dx 0 T/2 21 En tan x + In cot x dx I-0 0 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ENROL for this Course (Free) Enroll 439 Recommend Lessons (Like) E . Rate and Review the Course .Comments . Sharing with friends 15 68 26 ratings 7 reviews Share MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)