Let f : R R be a function such that f(x)+3f ( 2-x )= x, x R. Let the maximum value of f on R be . If the area of the region bounded by the curves g(x)=x2 and h(x)= x3, >0, is 2, then 30 3 is equal to .
Application of Integrals
Previous year questions with solutions · 2025 – 2026
Year-wise statistics questions · papers · average per paper · weightage
| Year | Questions | Papers | Avg / paper | Weightage |
|---|---|---|---|---|
| 2026 | 19 | 19 | 1 | 4.00% ▼ 5% vs last year |
| 2025 | 20 | 19 | 1.1 | 4.21% |
If the area of the region bounded by 16x2-9y2=144 and 8x-3y=24 is A, then 3 (A+6 e(3) ) is equal to .
Let the area of the region bounded by the curve y = \ x, x\, lines x = 0, x = 3 2, and the x-axis be A. Then, A + A2 is equal to .
Let the area of the bounded region \(x, y) : 0 9x y2, y 3x - 6 \ be A. Then 6A is equal to .
If the area of the region \(x, y) : |x - 5| y 4 x\ is A, then 3A is equal to .
The area of the region bounded by the curve y = \|x|, x|x-2|\, the x-axis and the lines x = -2 and x = 4 is equal to
If the area of the region \(x, y) : |4 - x2 | y x2, y 4, x 0 \ is ( 80 2 - ), , N, then + is equal to .
If the area of the larger portion bounded between the curves x2+y2=25 and y=|x-1| is 14(b +c), b,c , then b+c is equal to
Let the function, f(x)= cases-3ax2-2, & x<1\ a2+bx, & x 1 cases be differentiable for all x , where a>1, b . If the area of the region enclosed by y=f(x) and the line y=-20 is + 3, , Z, then the value of + is .