The curves f(x) = x and g(x) = x intersect infinitely many times, forming bounded regions of equal areas. The area of one such region is: - Mathematics MCQ Mathematics Mock Test - 10 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 102026Mathematics

11 attempts18% success rate1 mark

The curves f (x) = sin x and g (x) = cos x intersect infinitely many times, forming bounded regions of equal areas. The area of one such region is:

Solution & Step-by-step Explanation

The curves sin x and cos x intersect when sin x = cos x ⟹ tan x = 1 .Consecutive points of intersection are x = \frac{π}{4} and x = \frac{5 π}{4} .Area = \int_{π /4}^{5 π /4} ∣ sin x - cos x ∣ d x In the interval [\frac{π}{4}, \frac{5 π}{4}], sin x \geq cos x .Area = \int_{π /4}^{5 π /4} (sin x - cos x) d x Area = [- cos x - sin x]_{π /4}^{5 π /4} Area = [- cos \frac{5 π}{4} - sin \frac{5 π}{4}] - [- cos \frac{π}{4} - sin \frac{π}{4}] Area = [- (- \frac{1}{2}) - (- \frac{1}{2})] - [- \frac{1}{2} - \frac{1}{2}] Area = [\frac{1}{2} + \frac{1}{2}] + [\frac{1}{2} + \frac{1}{2}] Area = 2 + 2 = 22 sq. units.

Try it yourself before checking the explanation above.

The curves f (x) = sin x and g (x) = cos x intersect infinitely many times, forming bounded regions of equal areas. The area of one such region is:

2 sq. units

22 sq. units

π sq. units

2 π sq. units

Practice with timed mock tests and track your performance across Mathematics.