Mathematics

# $\displaystyle \overset{\pi/2}{\underset{0}{\int}} e^x \,\sin \,x \,dx$ is equal to

$\dfrac{e^{\pi/2} - 1}{2}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle I=\int x\sqrt{\frac{x^{2}+1}{x^{2}-1}}dx,$ then $I$ equals

• A. $\displaystyle \frac{1}{2}\sqrt{x^{4}-1}+\frac{1}{2}\sqrt{x^{4}+1}+C$
• B. $\displaystyle \sqrt{x^{4}-1}+\sin^{-1}\left ( x^{2} \right )+C$
• C. $\displaystyle \sqrt{x^{4}-1}+2\sin^{-1}\left ( x^{2} \right )+C$
• D. $\displaystyle \frac{1}{2}\sqrt{x^{4}-1}+\frac{1}{2}\log\left ( x^{2}+\sqrt{x^{4}-1} \right )+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle \int \frac{dx}{\left ( x-p \right )\sqrt{\left ( x-p \right )\left ( x-q \right )}} \displaystyle =-\frac{2}{p-q}\sqrt{\frac{x-a}{x-b}}+c$ then find $a$ and $b$ are respectively
• A. $p,q$
• B. $q,q^2$
• C. $p^2,q^2$
• D. $q,p$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$I=\displaystyle\int x^2\left(1-\dfrac{2}{x}\right)^2dx$. Evaluate the following functions w.r.t. x.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Find :
$\int { \dfrac { { se }c^{ 2 }x }{ { tan }^{ 2 }x+4 } } dx$

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