Mathematics

# $\overset { 1 }{ \underset { 0 }{ \int } } xe^x dx=$

$1$

##### SOLUTION
$I=\overset { 1 }{ \underset { 0 }{ \int } } xe^xdx..............(1)$
$\int xe^x=xe^x-\int1.e^xdx$
$=xe^x-e^x$
$=e^x(x-1)$
From (1)
$I=\overset { 1 }{ \underset { 0 }{ \int } } xe^xd^x-[e^x(x-1){ ] }_{ 0 }^{ 1 }$
$=e(1-1)-e^0(0-1)$
$=e\times0-1(-1)$
$=0+1$
$I=1$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
If $\displaystyle \int \frac{1}{x\sqrt{1-x^{3}}}dx=a\log \left | \frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1} \right |+b$, then a is equal to
• A. $\dfrac 23$
• B. $-\dfrac 13$
• C. $-\dfrac 23$
• D. $\dfrac 13$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following as limit of sums:
$\displaystyle \int_{0}^{2} (x^2 + 3) dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $f(a+b-x)=f(x)$, then $\displaystyle \int_a^bxf(x)dx$ is equal to
• A. $\dfrac {a+b}{2}\displaystyle \int_a^bf(b-x)dx$
• B. $\dfrac {a+b}{2}\displaystyle \int_a^bf(b+x)dx$
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• D. $\dfrac {a+b}{2}\displaystyle \int_a^bf(x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
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Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$