NIMCET 2024 Paper

Section: Mathematics

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Question : 12 of 120

Marks: +1, -0

Which of the following is TRUE?

If $f$ is continuous on $[a, b]$ , then $∫↙{a}↖{b} x f(x) \dx=x ∫↙{a}↖{b} f(x) \dx$
$∫↙{0}↖{3} e^{x^2} \dx=∫↙{0}↖{5} e^{x^2} \dx+∫↙{5}↖{3} e^{x^2} \dx$
If $f$ is continuous on $[a, b]$ , then $\;{d}/{d x} (∫↙{a}↖{b} f(x) \dx) =f(x)$
Both (1) and (2)

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