The area of the region bounded by Y -axis, y = x and y = x for 0 ≤ x ≤ π/4 is: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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The area of the region bounded by Y -axis, y = cos x and y = sin x for 0 \leq x \leq \frac{π}{4} is:

Solution & Step-by-step Explanation

The region is bounded by x = 0 (Y -axis) and the point where sin x = cos x, which is x = \frac{π}{4} .In the interval [0, π /4], cos x \geq sin x .Area = \int_{0}^{π /4} (cos x - sin x) d x $ = [sin x - (- cos x)]_{0}^{π /4} = [sin x + cos x]_{0}^{π /4} $ = (sin \frac{π}{4} + cos \frac{π}{4}) - (sin 0 + cos 0) = (\frac{1}{2} + \frac{1}{2}) - (0 + 1) = \frac{2}{2} - 1 = 2 - 1 sq. units.

Try it yourself before checking the explanation above.

The area of the region bounded by Y -axis, y = cos x and y = sin x for 0 \leq x \leq \frac{π}{4} is:

2 - 1 sq. units

2 sq. units

2 + 1 sq. units

2 - 2 sq. units

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