Exams › JEE Main › Maths
The vertical line x = b divides the region bounded by y = (1 - x)², y = 0 and x = 0 into a left part R1 (0 <= x <= b) and a right part R2 (b <= x <= 1) so that R1 - R2 = 1/4. Find b.
- 3/4
- 1/2
- 1/3
- 1/4
Correct answer: 1/2
Solution
Solving the two area conditions gives b = 1/2 (the other roots are complex).
Related JEE Main Maths questions
- For every b > 1, the area enclosed by the x-axis, the graph of y = f(x), and the vertical lines x = 1 and x = b is given by √(b² + 1) − √2. Then f(x) must be:
- The graphs of y = sin x and y = cos x meet at infinitely many points, forming repeated bounded regions of equal area. The area of one such region is
- Find the area bounded by the parametric curve x = a cos³ t, y = b sin³ t together with the positive x-axis and positive y-axis.
- Find the area enclosed by the curves y = e^x, y = e^(-x), and the vertical line x = 1, measured in square units.
- A straight line of the form y = mx divides into two equal parts the region bounded by the y-axis, the horizontal line y = 3/2, and the parabola y = 1 + 4x - x². What is the value of m?
- Find the area enclosed by the curve y = cos² x, the x-axis, and the vertical lines x = 0 and x = π over the interval (0, π).
⚔️ Practice JEE Main Maths free + battle 1v1 →