## Vineet Loomba is teaching live on Unacademy Plus

MoST IMPORTANT QUESTIONS IN APPLICATIONS OF INTEGRALS JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010 * Many of my students are pursuing courses in IITs, NITs, BITs etc unacademy * Currently running my own Coaching Institute for JEE Main and Advanced Search vineet loomba unacademy" on GOOGLE Follow me to access all the courses free of cost.

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Follow me on Unacademy for Next live Special Class Strategy for JEE Main and Advanced V Limits, Continuity, Differentiability v Sets, Relations and Functions Indefinite Integration Trigonometry V Definite Integratiorn VApplications of Derivatives Complex Number Permutations Combinations Binomial Theorem V Logarithmic Functions V Sequences Series V Straight Lines Applications of Integrals Circles (Detailed Course) Probability Most Important Questions in IIT-IEE Mathematics Parabola (Detailed Course) Ellipse (Detailed Course) V Inverse Trigonometry Upcoming Courses next month: Mathematical Reasoning Coordinate Geometry Differential Equations

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SPECIAL ANNOUNCEMENT Share useful links and advice with your learners... CRASH COURSE FOR JEE MAIN 2019 (JANUARY SESSION) Find courses & lessons 735 Courses IIT JEE 2,521 Courses Str Chemistry 797 Courses Details in Plus Tab wwEest HINDI Home My Library Plus Profile SUCCESS IN JEE MAIN ER. VINEET LoOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration The area bounded by the curves : y-4a (x + a) and y-4b (b-x) is : (A) 5(a+bs4ab(B) a+bV4ab (C)bv4ab(D) None of these SOLUTION: (B) The two curves are: =4a (x + a) 2b 2a and y-4b (b-x) Solving 4a(r+a) and y 4b (b-x) simultaneously, we get the coordinates of A and B Replacing values of x from (ii) and (i), we get using property-8] 2 3b 4b y2 = 4b (b-x) y2 -4a (x +) >A- (b-a, V4ab) and B(b-a,-4ab) 4ab shaded area 4b4a SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration: Determine the area enclosed by the two curves given by y-x + 1 and y-- + 1. Solution: Given curves are (1) and yx1 C(0, 1 curve (1) is the parabola having axis y curve (2) is the parabola having axis y (1) (2) 2x 0 x 0 From (1), x = 0 0 and vertex (-1, 0) 0 and vertex (1, 0) A (-1, 0) B (-1, 0) Required area -j (x1-x2) dy = f [(1-y2)-(y2-1)] dy 1t-sq. units SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration: Find the area bounded by the parabola y2 4x and the straight line x +y 3 Solution: Given curves are y2 -4x... (1) and x+y=3 D(3, 0) Required area OCDAOx -x2)dy 4 64 sq. units 3 2 12 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration : Find the area enclosed by the parabola (y -2x-1, the tangent to the parabola at (2,3) and x-axis Solution: Given parabola is (y -2 x1 Its axis is y 2 and vertex is (1, 2 et P ( From , 2(y-2)dy Gy1 y-3 y-2 P(2,3) dx 2(y-2) Q(-4,0)10 R(5,0) At P(2,3) dy1 Equation of tangent at P(2, 3) is y-3--(x-2) or, x-2y+4=0 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Line (ii) cuts the x-axis at (-4,0) and y-axis at (0, 2). Required area, RQPAR - (x-x2)dy -| _ _ +9y! (9-27 +27)-0-9 square units. 0 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Illustration: If the line y- mx divides the area enclosed by the lines x-0, y 0, x 3/2 and the curve 4x-x2 into two equal parts, then find the value of m y = 1 Solution The given curve is y-5(x- 2) Thus given curve is a parabola with vertex at (2,5) and axis x = 2 Given that area CBFC = Area CDEBC So area CDEBFC 2 Area CBFC 3/2 Area CDEBFC = | (1 + 4x-x*)dx 3 9) 9 39 2 48 8 unilts =|x + 2x"- 2 X y=1+4x-x2 3/2 39-18m, or m= 13 Area CBFC = | mxdx=- So we must have 4 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)