Mathematics

# The value of the definite integral $\underset{0}{\overset{\pi / 2}{\int}} \dfrac{sin 5x}{sin x} dx$ is :

$0$

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

#### Realted Questions

Q1 Multiple Correct Hard

Let $\displaystyle \mathrm{S}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}}\frac{\mathrm{n}}{\mathrm{n}^{2}+\mathrm{k}\mathrm{n}+\mathrm{k}^{2}}$ and $\displaystyle \mathrm{T}_{\mathrm{n}}=\sum_{\mathrm{k}=0}^{\mathrm{n}-1}\frac{\mathrm{n}}{\mathrm{n}^{2}+\mathrm{k}\mathrm{n}+\mathrm{k}^{2}}$ for $\mathrm{n}=1,2,3,\ \ldots$. Then,
• A. $\displaystyle \mathrm{S}_{\mathrm{n}}>\frac{\pi}{3\sqrt{3}}$
• B. $\displaystyle \mathrm{T}_{\mathrm{n}}<\frac{\pi}{3\sqrt{3}}$
• C. $\displaystyle \mathrm{S}_{\mathrm{n}}<\frac{\pi}{3\sqrt{3}}$
• D. $\displaystyle \mathrm{T}_{\mathrm{n}}>\frac{\pi}{3\sqrt{3}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\displaystyle\int \dfrac{x+\sin x}{1+\cos x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $I= \displaystyle \int_{1}^{\infty }\displaystyle \frac{x^{2}-2}{x^{3}\sqrt{x^{2}-1}}\: dx$, then $I$ equals
• A. $-1$
• B. $\pi /2$
• C. $\pi -\sqrt{3}$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve :
$\int 2^x . e^x dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Integrate:
$\int _{ 0 }^{ \infty }{ \dfrac { x\tan ^{ -1 }{ x } }{ { (1+{ x }^{ 2 }) }^{ 2 } } } dx$ equals ?
• A. $\pi/2$
• B. $\pi/6$
• C. $\pi/4$
• D. $\pi/8$