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Answer :
Final answer:
The particular solution for F(x) is F(x) = (62/3)x³ + 2x² - 10/3.
Explanation:
To find the particular solution for F(x) if F'(x) = 62x² + 4x, and the initial condition is F(2) = 11, we need to integrate the given derivative function. Using the power rule for integration, we integrate
62x² + 4x to get F(x) = (62/3)x³ + 2x² + C.
To determine the value of C, we use the initial condition F(2) = 11.
Plugging in x = 2 and F(x) = 11, we get the equation 11 = (62/3)(2³) + 2(2²) + C.
Simplifying this equation, we find C = -10/3. Therefore, the particular solution for F(x) is F(x) = (62/3)x³ + 2x² - 10/3.
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