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Definite Integration · 2021 · 17 Mar · Shift 2

3 Mathematics questions from this JEE Main paper

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2021 · 17 Mar · Shift 2
Mathematics
Definite Integration

Definite Integration · 2021 · 17 Mar · Shift 2

3 Mathematics questions from this JEE Main paper

Q23.Let f : R $\to$ R be defined as f(x) = e $-$ xsinx. If F : [0, 1] $\to$ R is a differentiable function with that F(x) = $\int_{0}^{x} f (t) d t$ , then the value of $\int_{0}^{1} (F^{'} (x) + f (x)) e^{x} d x$ lies in the interval
Mathematics · Definite Integration · MCQ
Q28.If the integral $\int_{0}^{10} \frac{[ s i n 2 π x ]}{e ^{x - [x]}} d x = α e^{- 1} + β e^{- \frac{1}{2}} + γ$ , where $α$ , $β$ , $γ$ are integers and [x] denotes the greatest integer less than or equal…
Mathematics · Definite Integration · MCQ
Q38.Let $I_{n} = \int_{1}^{e} x^{19} (lo g ∣ x ∣)^{n} d x$ , where n $\in$ N. If (20)I10 = $α$ I9 + $β$ I8, for natural numbers $α$ and $β$ , then $α - β$ equals to .
Mathematics · Definite Integration · Numerical