Mathematics

# The value of $\displaystyle \int \dfrac {dx}{(1+\sqrt {x})\sqrt {x-x^{2}}}$ is equal to

$\dfrac {2(\sqrt {x}+1)}{\sqrt {1-x}}+c$

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

#### Realted Questions

Q1 Single Correct Medium
$\int _ { 0 } ^ { \pi } \dfrac { \sin \theta + \cos \theta } { \sqrt { 1 + \sin 2 \theta } } d \theta =$
• A. $\pi + \lambda$ and $\lambda > 0$
• B. $\pi / 2$
• C. $\pi / 3$
• D. $\pi$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium

$\displaystyle \int_{0}^{\infty}\frac{x^{2}dx}{(1+x^{2})^{7/2}}=$
• A. 1/15
• B. -1/15
• C. $\displaystyle \frac{4}{15}$
• D. 2/15

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $I_{1} = \int_{0}^{1} 2^{x^{3}} dx, I_{2} = \int_{0}^{1}2^{x^{2}}dx, I_{3} = \int_{1}^{2}2^{x^{2}}dx$ and $I_{4} = \int_{1}^{2}2^{x^{3}}dx$, then
• A. $I_{2} > I_{1}$
• B. $I_{3} > I_{4}$
• C. $I_{1} > I_{3}$
• D. $I_{1} > I_{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral: $\displaystyle\int_{-1}^{1}|2x+1|\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
The value of $\displaystyle\int\limits_{-1}^{1}\sin ^{11}x.\cos^{12}x\ dx$.