📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

  • google app store apple app store

    • Question

      src="https://www.ixambee.com/questionimage/DCT1/1747288400-269.JPG" alt="" />
      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).

      Practice Next

      Relevant for Exams:

      ask-question