Mathematics

# If $g\left( x \right) =\int { { x }^{ x }\log _{ e }{ (ex)dx } }$ then  $g\left( \pi \right)$ equals

${\pi}^\pi$

##### SOLUTION
$\begin{array}{l} g\left( x \right) =\int _{ }^{ }{ { x^{ x } } } \left( { 1+\log { e^{ x } } } \right) dx \\ =\int _{ }^{ }{ d\left( { { x^{ x } } } \right) } \\ g\left( x \right) ={ x^{ x } } \\ g\left( \pi \right) ={ \pi ^{ \pi } } \end{array}$

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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 Medium
$\int sin^{5}x.cos^{100}x dx=$
• A. $-\frac{cos^{105}x}{105}+2\frac{cos^{103}x}{103}-\frac{cos^{101}x}{101}+c$
• B. $-\frac{cos^{105}x}{105}-2\frac{cos^{103}x}{103}+\frac{cos^{101}x}{101}+c$
• C. $\frac{cos^{105}x}{105}-2\frac{cos^{103}x}{103}+\frac{cos^{101}x}{101}+c$
• D. $\frac{cos^{105}x}{105}+2\frac{cos^{103}x}{103}-\frac{cos^{101}x}{101}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate $\displaystyle\int_0^{\displaystyle\sqrt{3}}{\frac{1}{1+x^2}.\sin^{-1}{\left(\frac{2x}{1+x^2}\right)}dx}$.
• A. $\displaystyle\frac{5}{72}\pi^2$
• B. $\displaystyle\frac{13}{144}\pi^2$
• C. $\displaystyle\frac{1}{12}\pi^2$
• D. $\displaystyle\frac{7}{72}\pi^2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Passage Medium
Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$

On the basis of above information, answer the following questions:

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate: $\displaystyle \int \dfrac{2 x}{\left(x^{2}+4\right)} d x$

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