MathsJEE Main 28 Jan 2026, Shift 1·Q13·MCQ·Moderate

Area under Curves · Area bounded by curves

The area of the region

R = \{(x, y) : xy \le 8,\ 1 \le y \le x^2,\ x \ge 0\}

is

(1) $\dfrac{1}{3}\left(49\log_e(2) - 15\right)$
(2) $\dfrac{2}{3}\left(20\log_e(2) + 9\right)$
(3) $\dfrac{2}{3}\left(24\log_e(2) - 7\right)$
(4) $\dfrac{1}{3}\left(40\log_e(2) + 27\right)$

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23 Jan 2026, Shift 1 · Q22Let the area of the region bounded by the curve y = x, x, lines x = 0, x = 3π/2, and the x-axis be A. Then, A + A2 is equal to .