Mathematics

# Value of $\displaystyle \int_{1}^{5} \left(\sqrt {x+2\sqrt {x-1}}+\sqrt {x-2(x-1)}\right)dx$ is

$\dfrac {8}{3}$

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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 Hard
Integrate $\displaystyle \int \dfrac{1}{x^{2/3}\sqrt{x^{2/3}-4}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of the integral I = $\begin{matrix} -2 \\ \int \\ 0 \end{matrix} x(1 - x)^n$ dx is equal
• A. $\dfrac{1}{n + 2}$
• B. $\dfrac{1}{n + 1} - \dfrac{1}{n + 2}$
• C. $\dfrac{1}{n + 1} - \dfrac{1}{n + 2}$
• D. $\dfrac{1}{n + 1}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve : $\displaystyle \underset{0}{\overset{2 \pi}{\int}} \dfrac{sin \theta \, d \theta}{a - b \, \cos \theta}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals
$\int { \cfrac { 1 }{ 5-4\cos { x } } } dx$

$\underset {n\rightarrow \infty}{lim}\dfrac{1^2+2^2+3^2+.....+n^2}{n^3}=.................$