Mathematics

The value of $$\displaystyle \int _ { 0 } ^ { 10 } e ^ { \operatorname { sgn } ( x - [ x ] ) } d x$$ equals (where $$\left[.\right]$$ represents the greatest integer function) 


ANSWER

$$10 e$$


SOLUTION
$$\displaystyle \int_0^{10} e^{sgn(x-[x])}dx$$ 
$$= \displaystyle \int_0^{10} e^{sgn\{x\}}dx$$             $$sgn(x) = \left\{\begin{matrix}1, & x > 0 \\  0,& x=0\\ -1, &x<0 \end{matrix}\right.$$
$$=\displaystyle \int_0^{10}e'dx$$       $$(\because \{x\} > 0)$$
$$=ex|_0^{10}$$
$$= 10e$$
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
The value of $$\int _{ { \pi  }/{ 4 } }^{ { \pi  }/{ 2 } }{ { e }^{ x }\left( \log { \sin { x }  } +\cot { x }  \right) dx } $$ is 
  • A. $${ e }^{ { \pi }/{ 4 } }\log { 2 } $$
  • B. $$-{ e }^{ { \pi }/{ 4 } }\log { 2 } $$
  • C. $$-\dfrac { 1 }{ 2 } { e }^{ { \pi }/{ 4 } }\log { 2 } $$
  • D. $$\dfrac { 1 }{ 2 } { e }^{ { \pi }/{ 4 } }\log { 2 } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Calculate the following integrals.
$$\displaystyle \int_{-\pi/2}^{\pi/2} \, | sin \, x | \, dx.$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate:
$$\displaystyle\int\limits_{0}^{2a}\dfrac{f(x)}{f(x)+f(2a-x)}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int x \tan^{-l} (x^{2})dx=$$
  • A. $$\displaystyle \frac{1}{2}[x^{2}\tan^{-1}(x^{2})+\log(1+x^{4})]+c$$
  • B. $$x^{2}\tan^{-1}(x^{2})-\displaystyle \frac{1}{2}\log(1+x^{4})+c$$
  • C. $$x^{2}\tan^{-1}(x^{2})+\displaystyle \frac{1}{2}\log(1+x^{4})+c$$
  • D. $$\displaystyle \frac{1}{2}[x^{2}\tan^{-1}(x^{2})-\frac{1}{2}\log(1+x^{4})]+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Solve:
$$\displaystyle\int_{1}^{2} \dfrac 2x\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer