Mathematics

$\displaystyle\int^{\lambda}_0\dfrac{y}{\sqrt{y+\lambda}}dy=?$

$\dfrac{2}{3}(2-\sqrt{2})\lambda \sqrt{\lambda}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

Q1 Multiple Correct Hard
For the function $f(x)=\overset { x }{ \underset{ 0}{{ \int} }}2|t|dt$ , the equation of tangents which are parallel to $2x - 2y + 3 = 0$ will be
• A. $y=x+\dfrac{1}{2}$
• B. $y=x-\dfrac{1}{2}$
• C. $y=x-\dfrac{1}{4}$
• D. $y=x+\dfrac{1}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral
$\int { \cfrac {2\cos { 4x } -\cos { 2x } }{ \sin { 4x } -\sin { 2x } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\displaystyle \int_{{\sqrt{ \ln2}}}^{{\sqrt{\ln3}}}\frac{x\sin x^{2}}{\sin x^{2}+\sin(\ln 6-x^{2})} dx$ is

• A. $\displaystyle \frac{1}{2}\ln\frac{3}{2}$
• B. $\displaystyle \ln\frac{3}{2}$
• C. $\displaystyle \frac{1}{6}\ln\frac{3}{2}$
• D. $\displaystyle \frac{1}{4}\ln\frac{3}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve :
$I = \displaystyle\int \dfrac {x+9}{x^2+5} dx$

$\int \frac{1}{1+x}\;dx$