Mathematics

# If $\int { \frac { dx }{ { x }^{ 3 }{ (x-1) }^{ 1/2 } } } =\frac { \sqrt { x-1 } (3x+2) }{ { 4x }^{ 2 } } +K{ tan }^{ -1 }\sqrt { x-1 } +c$ then the valuie of K is -

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\int {{{dx} \over {{x^4} - 1}}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int \dfrac{2x\log(1+x^2)}{1+x^2}dx$
• A. $\log(1+x^2)+c$
• B. $2\log(1+x^2)+c$
• C. none of these
• D. $\dfrac{[\log(1+x^2)]^2}{2}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Let $f\left( x \right) = \sin 2x\,\sin \left( {\frac{\pi }{2}\cos x} \right)\,\,and\,\,g\left( x \right) = \frac{{f\left( x \right)}}{{2x - \pi }}$
$\int_0^\pi {f\left( x \right)dx = }$
• A. $\frac{8}{\pi }$
• B. $\frac{8}{{{\pi ^2}}}$
• C. $\frac{{16}}{{{\pi ^2}}}$
• D.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Compute the integral $\displaystyle \int_{1}^{\sqrt{3}}\frac{\sqrt{1+x^{2}}}{x^{2}}dx$
• A. $\displaystyle \frac{2}{\sqrt{3}}+\ln\frac{2+\sqrt{3}}{1+\sqrt{3}}$
• B. $\displaystyle \sqrt{2}-\frac{\sqrt 2}{{3}}+\ln\frac{2+\sqrt{3}}{1-\sqrt{3}}$
• C. $\displaystyle \sqrt{2}+{2}-\ln\frac{2+\sqrt{3}}{1+\sqrt{3}}$
• D. $\displaystyle \sqrt{2}-\frac{2}{\sqrt{3}}+\ln\frac{2+\sqrt{3}}{1+\sqrt{3}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int _ { 0 } ^ { 4 } \frac { \sin x ^ { 2 } d x } { \sin ( x - 4 ) ^ { 2 } + \sin x ^ { 2 } }$ is equal to
• A. 4
• B. 8
• C. 16
• D. 2