Mathematics

# $\displaystyle \int \dfrac{1}{\sqrt{4 + x^2}} dx$

##### ANSWER

$\dfarc{1}{2} \tan^{-1} \left(\dfarc{x}{2}\right) + c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate the given integral
$\int { x.cosec ^{ 2 }{ x } } dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of the integral $\int_{-3 \pi / 4}^{5 \pi / 4} \dfrac{(\sin x+\cos x)}{e^{x-\pi / 4}+1} d x$ is
• A. $1$
• B. $2$
• C. None of these
• D. $0$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int x\sec x^{2}dx$ is equal to
• A. $\displaystyle \frac{x^{2}}{2}\log \left ( \sec x^{2}+\tan x^{2} \right )+k$
• B. $\displaystyle 2\log \left ( \sec x^{2}+\tan x^{2} \right )+k$
• C. none of these
• D. $\displaystyle \frac{1}{2}\log \left ( \sec x^{2}+\tan x^{2} \right )+k$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral as the limit of sum:
$\displaystyle\int^2_0x^3dx$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
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 $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020