Which of the following is true? - Solved

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Question 39

Mathematics Continuous function Medium

Which of the following is true?

(A) If \(f\) is continuous on \([a, b]\), then \(\int_a^b f(x) dx = \int_a^b x f(x) dx\)

(B) \(\int_0^3 e^{x^2} dx = \int_0^5 e^{x^2} dx + \int_5^3 e^{x^2} dx\)

(C) If \(f\) is continuous on \([a, b]\), then \(\frac{d}{dx}\left(\int_a^b f(x) dx\right) = f(x)\)

(D) Both (1) and (2)

✓ Correct Answer: Option B Verified Solution

Correct Option is B. Practice regular variations of this Continuous function concept to build speed and accuracy.

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