Mathematics

# Number of real solution of the given equation for $x$, $\int x^{2}\ e^{x}dx=0$

##### SOLUTION
$\int_{}^{} {{x^2}{e^x}dx = 0}$
$\Rightarrow {x^2}{e^x} - \int_{}^{} {2x{e^x}dx} = 0$
$\Rightarrow {x^2}{e^x} - 2\left[ {x{e^x} - \int_{}^{} {{e^x}dx} } \right] = 0$
$\Rightarrow {x^2}{e^x} - 2x{e^x} + 2{e^x} = 0$
$\Rightarrow {e^x}\left( {{x^2} - 2x + 2} \right) = 0$
$\Rightarrow \left( {{x^2} - 2x + 2} \right) = 0$
Now, $D = {\left( { - 2} \right)^2} - 4 \times 1 \times 2 = 4 - 8 = - 4 < 0$
So, it has no real roots

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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#### Realted Questions

Q1 Subjective Medium
Evaluate the following : $\displaystyle\int \dfrac{1}{\sqrt{8-3x+2x^{2}}}.dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int \dfrac {dx}{(x^{2} + 4x + 5)^{2}}$ is equal to
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• C. $\dfrac {1}{2}\left [\tan^{-1}(x + 1) - \dfrac {x + 2}{x^{2} + 4x + 5}\right ] + c$
• D. $\dfrac {1}{2}\left [\tan^{-1}(x + 2) + \dfrac {x + 2}{x^{2} + 4x + 5}\right ] + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
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Q4 Subjective Hard
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