Mathematics

# Solve :$\int _{ 0 }^{ \frac{1}{2} }{ \dfrac { x\sin ^{ -1 }{ x } }{ \sqrt { 1-{ x }^{ 2 } } } dx},(x\not=1)$

$\dfrac { 1 }{ 2 } -\dfrac { \sqrt { 3 } \pi }{ 12 }$

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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
$\text { Evaluate: } \displaystyle \int e^{x}\left(\dfrac{\sin 4 x-4}{1-\cos 4 x}\right) d x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int { { e }^{ x }{ \left( \frac { x+2 }{ x+4 } \right) }^{ 2 }dx }$ is equal to
• A. $\displaystyle { e }^{ x }{ \left( \frac { x+2 }{ x+4 } \right) }+c$
• B. $\displaystyle \frac { { e }^{ x } }{ x+4 } +c$
• C. none of these
• D. $\displaystyle \frac { x{ e }^{ x } }{ x+4 } +c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The solution of $x$ of the equation $\displaystyle \int_{\sqrt{2}}^{x}{\dfrac{dt}{t\sqrt{t^{2}-1}}}=\dfrac{\pi}{2}$ is
• A. $2$
• B. $\pi$
• C. $-\sqrt{2}$
• D. $2\sqrt{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium

Evaluate the following definite integral:

$\displaystyle \int _2^3 x^2+2x+5 dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
Case II If $p>0$, then put $\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$
Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$