Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x) , x-axis and the ordinates x = π/4 and x = β > π/4 is - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let f (x) be a non-negative continuous function such that the area bounded by the curve y = f (x), x-axis and the ordinates x = π /4 and x = β > π /4 is β sin β + \frac{π}{4} cos β + 2 β . Then f (π /2) is:

Solution & Step-by-step Explanation

The area is given by \int_{π /4}^{β} f (x) d x = β sin β + \frac{π}{4} cos β + 2 β .Differentiating both sides with respect to β : f (β) = \frac{d}{d β} (β sin β + \frac{π}{4} cos β + 2 β) f (β) = (1 \cdot sin β + β cos β) - \frac{π}{4} sin β + 2 Now, substitute β = π /2 : f (π /2) = sin (π /2) + \frac{π}{2} cos (π /2) - \frac{π}{4} sin (π /2) + 2 f (π /2) = 1 + \frac{π}{2} (0) - \frac{π}{4} (1) + 2 f (π /2) = 1 - \frac{π}{4} + 2

Try it yourself before checking the explanation above.

Let f (x) be a non-negative continuous function such that the area bounded by the curve y = f (x), x-axis and the ordinates x = π /4 and x = β > π /4 is β sin β + \frac{π}{4} cos β + 2 β . Then f (π /2) is:

\frac{π}{4} - 2 + 1

2 - \frac{π}{4} + 1

1 - \frac{π}{4} - 2

1 - \frac{π}{4} + 2

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