Question:
\( \int dx = x^2 + C \)
\( \int dx = x^2 + C \)
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The integral \( \int dx \) represents the antiderivative of 1 with respect to \( x \), and its result is simply \( x + C \), not \( x^2 + C \).
Updated On: Feb 2, 2026
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Solution and Explanation
Step 1: Recognizing the error in the statement.
The given statement is incorrect. The integral \( \int dx \) represents the antiderivative of 1 with respect to \( x \). The correct antiderivative of 1 is \( x \), not \( x^2 \). Step 2: Correcting the statement.
The correct result of \( \int dx \) is: \[ \int dx = x + C \] where \( C \) is the constant of integration. Step 3: Conclusion.
Thus, the statement is False, because the correct integral is \( \int dx = x + C \), not \( x^2 + C \).
The given statement is incorrect. The integral \( \int dx \) represents the antiderivative of 1 with respect to \( x \). The correct antiderivative of 1 is \( x \), not \( x^2 \). Step 2: Correcting the statement.
The correct result of \( \int dx \) is: \[ \int dx = x + C \] where \( C \) is the constant of integration. Step 3: Conclusion.
Thus, the statement is False, because the correct integral is \( \int dx = x + C \), not \( x^2 + C \).
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