Application of Integrals

JEE Main 2024 (Online) 29th January Evening ShiftNumericalEasy📈 Topic in 72% papers+4

Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let the area of the region \(x, y): 0 x 3, 0 y \x2+2, 2x+2 \ \ be A. Then 12 A is equal to .

Answer

164

[figure]

x2+2 2x+2 0 x 2 (curves meet at (0, 2) and (2, 6))

upper boundary: y=x2+2 on [0, 2], y=2x+2 on [2, 3]

A= 02(x2+2) dx+ 23(2x+2) dx

= [ x33+2x ]02+ [x2+2x ]23= 203+7= 413

12A=164

Answer: 164

Ques. 2JEE Main 2024, 27 January (Morning Shift)

Let the area of the region \(x, y): x-2y+4 0, x+2y2 0, x+4y2 8, y 0 \ be mn, where m and n are coprime numbers. Then m+n is equal to .

Ques. 3JEE Main 2024, 27 January (Evening Shift)

If the area of the region \(x,y):0 y \2x,6x-x2 \ \ is A, then 12A is equal to .

All JEE Main Mathematics chapters