Mathematics

# The value of definite integral $\displaystyle \int _{ 0 }^{ 1/3 }{ \dfrac { ln\left( 1+3x \right) }{ 1+{ 9x }^{ 2 } } } dx$ equals

$\dfrac { \pi }{ 8 } \ell n2$

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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
$\displaystyle \int \tan^{-1} x dx=$__________$+c$.
• A. $x\tan^{-1}x+\dfrac{1}{2}log\left|\dfrac{\tan^{-1}x}{x^2+1}\right|$
• B. $x\tan^{-1}x+\dfrac{1}{2}log\left|x^2+1\right|$
• C. $\dfrac{1}{1+x^2}$
• D. $x\tan^{-1}x-\dfrac{1}{2}log\left|x^2+1\right|$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate: $\displaystyle\int_{0}^{\pi/4}\sin^{3}2t\cos 2t\ dt$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate the integral
$\displaystyle \int_{\frac{\sqrt{2}}{3}}^{ \frac{\sqrt{3}}{3}}\displaystyle \frac{dx}{\sqrt{4-9x^{2}}}$
• A. $\displaystyle \frac{\pi}{3}$
• B. $\displaystyle \frac{\pi}{4}$
• C. $\displaystyle \frac{7\pi}{30}$
• D. $\displaystyle \frac{\pi}{36}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

$\displaystyle \frac{x^{2}+2x+3}{x^{3}}=\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x^{3}}\Rightarrow A+B-C=$
• A. 6
• B. 3
• C. 1
• D.

Evaluate $\displaystyle \int_0^{10\pi}|\sin\,x|dx$