Mathematics

# The solution of $x$ of the equation $\displaystyle \int_{\sqrt{2}}^{x}{\dfrac{dt}{t\sqrt{t^{2}-1}}}=\dfrac{\pi}{2}$ is

##### ANSWER

$2\sqrt{2}$

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

#### Realted Questions

Q1 Subjective Medium
Integrate the function    $\displaystyle \frac {2+\sin 2x}{1+\cos 2x}e^x$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
What is $\displaystyle\int { \left( x\cos { x } +\sin { x } \right) dx }$ equal to?
Where $c$ is an arbitrary constant
• A. $x\cos { x } +c$
• B. $-x\sin { x } +c$
• C. $-x\cos { x } +c$
• D. $x\sin { x } +c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Assertion & Reason Medium
##### ASSERTION

The value of $\displaystyle \int_{0}^{1} \tan ^{-1} \dfrac{2 x-1}{\left(1+x-x^{2}\right)} d x=0$

##### REASON

$\int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x$

• A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• B. Assertion is correct but Reason is incorrect
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Obtain $\displaystyle \int_{1}^{e}(x^2 - x)dx$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
If $n\rightarrow \infty$ then the limit of series in $n$ can be evaluated by following the rule : $\displaystyle \lim_{n\rightarrow \infty}\sum_{r=an+b}^{cn+d}\frac{1}{n}f\left ( \frac{r}{n} \right )=\int_{a}^{c}f(x)dx,$
where in $LHS$, $\dfrac{r}{n}$ is replaced by $x$,
$\dfrac{1}{n}$ by $dx$
and the lower and upper limits are $\lim_{n\rightarrow \infty }\dfrac{an+b}{n}\, and \, \lim_{n\rightarrow \infty }\dfrac{cn+d}{n}$ respectively.
Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020