The value of the definite integral _0^1 e^ e^x (1 + x , , e^x )dx… - Vidyadip

MCQ

The value of the definite integral $\int\limits_0^1 {{e^{{e^x}}}(1 + x\,\cdot\,{e^x})dx} $ is equal to

✓
$e^e$
B
$e^e - e$
C
$e^e - 1$
D
$e$

✓

Answer

Correct option: A.

$e^e$

a
start with $e^x = t$ and use $\int {{e^x}\left( {f(x) + f'(x)} \right)\,dx} $ $= e^x f (x)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_0^\pi {{{\sin }^5}\left( {\frac{x}{2}} \right)\,dx} $ equals

If $A = \left[ {\begin{array}{*{20}{c}}2&3\\4&6\end{array}} \right]$, then ${A^{ - 1}}$=

The differential equation of all ‘Simple Harmonic Motions’ of given period $\frac{2\pi}{\text{n}}$ is:

Area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x=0$ and $x=2$ is

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b ∈ T. Then, R is:

If the binary operation $\times$ is defind on the set $Q +$ of all positive rational numbers by $\text{a}\times\text{b}=\frac{\text{ab}}{4}.$ Then, $3\times\Big(\frac{1}{5}\times\frac{1}{2}\Big)$ is equal to:

Evaluate $\begin{bmatrix}8\text{x}+1&2\text{x}-2\\\text{x}^2-1&3\text{x}+5\end{bmatrix}$ is:

Let f(x) = |x| + |x - 1|, then:

The following system of linear equations $2 x+3 y+2 z=9$ ; $3 x+2 y+2 z=9$ ;$x-y+4 z=8$

Let $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}$ and $\overrightarrow{ c }=\hat{ i }-\hat{ j }+\hat{ k }$ be three given vectors. Let $\vec{v}$ be a vector in the plane of $\vec{a}$ and $\overrightarrow{ b }$ whose projection on $\overrightarrow{ c }$ is $\frac{2}{\sqrt{3}}$. If $\overrightarrow{ v } . \hat{ j }=7$, then $\overrightarrow{ v } \cdot(\hat{ i }+\hat{ k })$ is equal to