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For a double sided function, which is odd, what will be the integral of the function from -infinity to +infinity equal to?
- a)Non-zero Finite
- b)Zero
- c)Infinite
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
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For a double sided function, which is odd, what will be the integral o...
For an odd function, f(-x) = -f(x), thus the integrals will cancel each other, giving zero.
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For a double sided function, which is odd, what will be the integral o...
Explanation:
Double Sided Function:
- A double sided function is a function that is symmetric about the y-axis. This means that for every input x, there is a corresponding input -x that produces the same output.
Odd Function:
- An odd function is a function that satisfies the property f(-x) = -f(x) for all x in its domain. In other words, the function is symmetric about the origin.
Integral of an Odd Function:
- When integrating an odd function over a symmetric interval such as from -infinity to +infinity, the positive and negative areas on each side of the y-axis cancel each other out.
- This cancellation results in the integral of an odd function over a symmetric interval being equal to zero.
Therefore, the integral of a double sided odd function from -infinity to +infinity will be zero (option B).
Double Sided Function:
- A double sided function is a function that is symmetric about the y-axis. This means that for every input x, there is a corresponding input -x that produces the same output.
Odd Function:
- An odd function is a function that satisfies the property f(-x) = -f(x) for all x in its domain. In other words, the function is symmetric about the origin.
Integral of an Odd Function:
- When integrating an odd function over a symmetric interval such as from -infinity to +infinity, the positive and negative areas on each side of the y-axis cancel each other out.
- This cancellation results in the integral of an odd function over a symmetric interval being equal to zero.
Therefore, the integral of a double sided odd function from -infinity to +infinity will be zero (option B).
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