Mathematics

# If $\int _{ 0 }^{ a }{ \quad } \frac { dx }{ \sqrt { x+a } +\sqrt { x } } =\int _{ 0 }^{ \pi /8 }{ \frac { 2\tan { \theta } }{ \sin { 2\theta } } d\theta } ,\quad then\quad value\quad of\quad 'a'\quad is\quad equal\quad to\quad \left( a\quad >\quad 0 \right)$

$\frac { 3 }{ 4 }$

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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
The value of the integral $\displaystyle \int_{0}^{3}\displaystyle \frac{dx}{\sqrt{x+1}+\sqrt{5x+1}}$ is
• A. $11/15$
• B. $14/15$
• C. $2/5$
• D. none of these

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate:$\displaystyle\int \frac{cos\,x}{\sqrt{9sin^{2}x-1}}dx$
• A. $\log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C$
• B. ${3} \log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C$
• C. none of these
• D. $\dfrac{1}{3} \log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 One Word Hard
If $\displaystyle \int_{0}^{1}\frac{dx}{(1+x)(2+x)\sqrt{x(1-x)}}=\frac{\pi A}{\sqrt{6}(\sqrt{3}+1) (157)}$, then $A$ is equal to

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int_{0}^{1}{}{(2x^2 +x+1)}dx$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$