Question

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    A π Correct Answer Incorrect Answer
    B 1/2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer

    Solution

    First, let's determine if the function f(x) is odd or even. A function is even if f(−x)=f(x). A function is odd if f(−x)=−f(x). Let's evaluate f(−x): f(−x)=(−x)2sin(−x) f(−x)=x2(−sinx) f(−x)=−x2sinx f(−x)=−f(x) Since f(−x)=−f(x), the functionf(x) = x2sin(x)is an odd function. For an odd function f(x), the definite integral over a symmetric interval [−a, a] is always zero: Therefore, the correct answer is option (D).

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