-01 e -x dx -A- 1B- e 2- eC- 2D- -2

The correct option is C 2 Let x=t^2 ⇒ dx=2tdt Thus, integration becomes 2∫_0^1te^tdt =2[(t 1)e^t]_0^1=2 ...

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Standard XII

Mathematics

Binomial Coefficients

∫01 e √x dx =...

Question

$\int_{0}^{1} e^{\sqrt{x}} d x =$

$- 2$

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$e^{2} - e$

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$2$

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Solution

The correct option is C
$2$

Let $x = t^{2}$

$\Rightarrow d x = 2 t d t$

Thus, integration becomes

$2 \int_{0}^{1} t e^{t} d t$

$= 2 [(t - 1) e^{t}]_{0}^{1} = 2$

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∫10e√xdx=

The correct option is C 2 Let x=t2 ⇒dx=2tdt Thus, integration becomes 2∫10tetdt =2[(t−1)et]10=2

$\int_{0}^{1} e^{\sqrt{x}} d x =$

The correct option is C
$2$

Let $x = t^{2}$

$\Rightarrow d x = 2 t d t$

Thus, integration becomes

$2 \int_{0}^{1} t e^{t} d t$

$= 2 [(t - 1) e^{t}]_{0}^{1} = 2$