Given below are two statements. Statement - 1 : _ 0 ^ [x] 4^ x-[x] d x= 3[x] 2 2…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Given below are two statements.
Statement - 1 : \(\int_{0}^{[x]} 4^{x-[x]} d x=\frac{3[x]}{2 \log 2}\)
Statement - 2 : \(\int_{1}^{[x]} \mathrm{a}^{x-[x]} \mathrm{dx}=[\mathrm{x}] \int_{1}^{1} \mathrm{a}^{\mathrm{x}-[\mathrm{x}]} \mathrm{dx}\)
In the light of the above statements, choose the correct answer from the options given below:
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true but Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(C) Statement - 1 is true and Statement - 2 is false
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