Mathematics

# $\underset{n - 1}{\overset{100}{\sum}} \underset{n - 1}{\overset{n}{\int}} \, e^{x - [x]} dx$ =

$\dfrac{e^{100} - 1}{e - 1}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int e^{e^x} . e^x dx =$ __________$+c$
• A. $\dfrac{1}{2}e^2.e^x$
• B. $\dfrac{1}{2}e^{e^x}$
• C. $(e^{e^x})^2$
• D. $e^{e^x}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \dfrac{(3x^3+1)dx}{x(x\cdot e^{x^3}+1)}$ is equal to?
• A. $ln\left|\dfrac{xe^{x^3}}{xe^{x^3}+1}\right|+C$
• B. $ln\left|\dfrac{xe^{x^3}}{xe^{x^3}-1}\right|+C$
• C. $ln\left|\dfrac{xe^{x^3}+1}{xe^{x^3}}\right|+C$
• D. $ln \left|\dfrac{xe^{x^3}-1}{xe^{x^3}}\right|+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle\int \dfrac{\sin\theta +\cos\theta}{\sqrt{\sin 2\theta}}d\theta$ equals:
• A. $\tan^{-1}(\sqrt{2\tan \theta}+1)-\tan^{-1}(\sqrt{2\tan \theta}-1)+c$
• B. $\tan^{-1}(\sqrt{2\tan \theta}+1)-\tan^{-1}(\sqrt{-2\tan \theta}-1)+c$
• C. $\tan^{-1}(\sqrt{-2\tan \theta}+1)+\tan^{-1}(\sqrt{2\tan \theta}-1)+c$
• D. $\tan^{-1}(\sqrt{2\tan \theta}+1)+\tan^{-1}(\sqrt{2\tan \theta}-1)+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:
$\int_{}^{} {\frac{{dx}}{{\sqrt {1 - {e^{2x}}} }}}$

$\int \frac{x}{x^2 + a^2} \;dx$