Mathematics

The value of $$\int_{0}^{1}\dfrac{dx}{e^{x}+e^{-x}}$$ is


ANSWER

$$\tan^{-1}\left(\dfrac{1-e}{1+e}\right)$$


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 84
Enroll Now For FREE

Realted Questions

Q1 Subjective Hard
Solve: $$\displaystyle \overset{\frac{\pi}{2}}{\underset{0}{\int}} \sqrt{\cos \theta}\cdot \sin^3 \theta d\theta$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
Find the general solution of $$\frac{{dy}}{{dx}} = \frac{{2y}}{x}$$
  • A. $$ y=e^{5\log x +c}$$
  • B. $$ y=e^{3\log x +c}$$
  • C. None of these
  • D. $$ y=e^{2\log x +c}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Evaluate $$\displaystyle\int\displaystyle\dfrac{1}{e^x-1}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
If $$\displaystyle \int\frac{2Cosx-3Sinx}{3Sinx+2Cosx}dx= A \log|3sinx+$$$$2cosx|+ BX+C$$, then $$A=\ldots\ldots\ldots.,B=\ldots\ldots\ldots\ldots$$,
  • A. $$\displaystyle \frac{1}{13}, -\displaystyle \frac{5}{13}$$
  • B. $$\displaystyle 12, -\displaystyle \frac{5}{13}$$
  • C. $$\displaystyle \frac{12}{13},\frac{5}{13}$$
  • D. $$\displaystyle \frac{12}{13},-\frac{5}{13}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate :
$$\displaystyle \int \dfrac {1}{(x + 3)\sqrt {x + 2}}dx$$, on $$x\, \in I \subset (-2, \infty)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer