Answer is: option2
2.397Solution:
Since f is an antiderivative of \( \frac{\sqrt{x}}{1 + x^3} \), that means:
\( f(x) = \int \frac{\sqrt{x}}{1 + x^3} dx + C \)
Given \( f(1) = 2 \), we can compute the value of \( f(3) \) using the Fundamental Theorem of Calculus:
\( f(3) = f(1) + \int_1^3 \frac{\sqrt{x}}{1 + x^3} dx \)
Using a graphing calculator, we get:
\( \int_1^3 \frac{\sqrt{x}}{1 + x^3} dx = 0.397 \)
\( f(3) = f(1) + \int_1^3 \frac{\sqrt{x}}{1 + x^3} dx = 2 + 0.397 = \boxed{2.397} \)
Hence option B