Mathematics

# If $I_1=\displaystyle \int_{e}^{e^{2}}\dfrac{dx}{\ln\ x}$ and $\displaystyle I_2=\int_{1}^{2}\dfrac{e^{x}}{x}\ dx$, then

$I_1=I_2$

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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
$\displaystyle \int\frac{a^{x}}{\sqrt{1-a^{2x}}}dx=$
• A. ${\dfrac{1}{\log a}\sin}h(a^{x})+c$
• B. $\sin^{-1}(a^{x})+c$
• C. $\log a \sin^{-1}(a^{x})+c$
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Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int_{-\pi/2}^{\pi/2} \dfrac{dx}{\theta^{sin x} + 1}$ is equal to
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• B.
• C. 1
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1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int \sqrt {1 + \sec x} dx$ is
• A. $\sin^{-1} (\sqrt {2}\sin x) + C$
• B. $2\sin^{-1} (\sqrt {2}\sin x) + C$
• C. $\sin^{-1} \left(\sqrt {2}\sin \dfrac x2\right) + C$
• D. $2\sin^{-1} \left(\sqrt {2}\sin \dfrac x2\right) + C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function   $\displaystyle \frac {\cos x}{\sqrt {1+\sin x}}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
Solve $\displaystyle\int {x{{\tan }^{ - 1}}x\,dx}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020