Mathematics

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


ANSWER

$${\pi}^\pi$$


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

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

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. $$\frac{cos^{105}x}{105}+2\frac{cos^{103}x}{103}-\frac{cos^{101}x}{101}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle\frac{7}{72}\pi^2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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: 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Integrate the rational function   $$\cfrac {3x-1}{(x-1)(x-2)(x-3)}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer