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Application of Integrals · Question 5

JEE Advanced 2024 Paper 2MCQMedium📈 Topic in 33% papers+4−1
1

Let S= \(x,y) R R: x 0, y 0, y2 4x, y2 12-2x and 3y+ 8 x 5 8 \. If the area of the region S is 2, then is equal to

  1. 172
  2. 173
  3. 174
  4. 175

Answer

(2) 173

Solution

Find which right boundary is active and integrate along y.

y2=4x and y2=12-2x meet at x=2, y=2 2; the line 3y+2 2x=10 2 also passes through (2,2 2) and meets y=0 at x=5 (before the parabola's x=6).

Line: x=5- 3y2 2. (6- y22 )- (5- 3y2 2 )=- 12 (y-2 2 ) (y+ 1 2 ) 0 on [0,2 2], so the line is the right boundary.

Area = 02 2 (5- 3y2 2- y24 )dy=10 2-3 2- 4 23= 173 2.

= 173. Answer: (B)

JEE Advanced 2024 Paper 2

Keep practising — Application of Integrals

2

Let be the area of the region enclosed between the curves C1, C2, and the lines x= 1 and x= 4. Then the value of - 1 e ( -2 e- 2 ) is .

JEE Advanced 2026 Paper 2
3

If is the area of the common region that lies inside both the given ellipses, then the value of is .

JEE Advanced 2026 Paper 2
4

Let R denote the set of all real numbers. Then the area of the region \(x,y) R R:x>0, y> 1x, 5x-4y-1>0, 4x+4y-17<0 \ is

  1. 1716- e 4
  2. 338- e 4
  3. 578- e 4
  4. 172- e 4
JEE Advanced 2025 Paper 2
5

Let S denote the locus of the mid-points of those chords of the parabola y2=x, such that the area of the region enclosed between the parabola and the chord is 43. Let R denote the region lying in the first quadrant, enclosed by the parabola y2=x, the curve S, and the lines x=1 and x=4. Then which of the following statements is (are) TRUE?

  1. (4, 3) S
  2. (5, 2) S
  3. Area of R is 143-2 3
  4. Area of R is 143- 3
JEE Advanced 2025 Paper 2

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