Exams › JEE Main › Maths
Find the area bounded by the curve f(x) = |tan x + cot x| - |tan x - cot x|, the lines x = 0 and x = pi/2, and the x-axis.
- ln sqrt(2)
- 2 ln sqrt(2)
- ln 4
- sqrt(2) ln 2
Correct answer: ln 4
Solution
Splitting at pi/4 gives area = integral of 2 tan x on (0, pi/4) plus integral of 2 cot x on (pi/4, pi/2), each equal to ln 2, totalling ln 4.
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 →