Question

Let f(x) be an antiderivative of sin³ x if f(1) = 0. What is the value of f(0)?

a) 0
b) 1
c) -1
d) 2

Answer 1

The question requires finding f(0) based on the antiderivative of sin³ x with the condition f(1) = 0. However, without the explicit integrated form of sin³ x, we cannot accurately determine the value of f(0).

Step-by-step explanation:

The student's question asks about finding the value of f(0) given that f(x) is an antiderivative of sin³ x and f(1) = 0. To solve this, we would first need to find an explicit formula for f(x), integrate sin³ x with respect to x, and then apply the initial condition f(1) = 0 to solve for any constants of integration. Finally, we would evaluate f(0) to find the desired value.

However, the provided information is incomplete and doesn't give a direct way to solve for f(x). It's also important to note that the items from the reference information provided do not directly apply to the computation of the antiderivative of sin³ x. Therefore, without additional context or clarification on the integration process for sin³ x, an accurate solution for f(0) cannot be provided.