Mathematics

# Evaluate:$\int { \sqrt { { x }^{ 2 }-16 } } \ dx$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
The value $\displaystyle \sqrt{2}\int\frac{\sin x dx}{\sin(x-\frac{\pi}{4})}$ is
• A. $x-\displaystyle \log|\sin(x-\frac{\pi}{4})|+C$
• B. $\displaystyle x- \log|\cos(x-\frac{\pi}{4})|+C$
• C. $\displaystyle x+ \log|\cos(x-\frac{\pi}{4})|+C$
• D. $\displaystyle x+ \log|\sin(x-\frac{\pi}{4})|+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve:
$\int {\dfrac{{{x^3} - 4{x^2} + 6x + 5}}{{{x^2} - 2x + 3}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle \int_{0}^{\infty }\frac{e^{-ax}\sin bx}{x}\:dx= \tan^{-1}\left ( b/a \right )$ then the value of $\displaystyle \int_{0}^{\infty }\frac{\sin ^2ax}{x^2}\:dx$ equals, $a\neq 0$
• A. $\displaystyle \frac{\pi a}{3}$
• B. $\displaystyle \frac{\pi a^2}{2}$
• C. $\displaystyle \frac{\pi^2a}{2}$
• D. $\displaystyle \frac{\pi a}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int {\dfrac{{2 - 3\sin x}}{{{{\cos }^2}x}}dx}$

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 $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$