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First, evaluate the indefinite integral ∫ 4x / √(x²-1) dx using u-substitution.Let u = x² - 1, then du = 2x dx, so 4x dx = 2 du.The integral becomes ∫ 2/√(u) du = 2 ∫ u^(-1/2) du = 2 * (u^(1/2) / (1/2)) + C = 4√(u) + C.Substitute back u = x² - 1: 4√(x² - 1) + C.Now, evaluate the definite integral from √2 to 4:[4√(x² - 1)] from √2 to 4 = 4√(4² - 1) - 4√((√2)² - 1)= 4√(16 - 1) - 4√(2 - 1)= 4√15 - 4√1 = 4√15 - 4 = 4(√15 - 1).The mathematically correct result is 4(√15 - 1). The highlighted option B is 4(√2 - 1). There is a significant numerical discrepancy between the calculated result and the provided option.