Mathematics

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


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$$0$$


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Single Correct Medium Published on 17th 09, 2020
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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,
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  • D. $$\displaystyle \mathrm{T}_{\mathrm{n}}>\frac{\pi}{3\sqrt{3}}$$

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1 Verified Answer | Published on 17th 09, 2020

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

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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
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Solve :
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Q5 Single Correct Medium
Integrate:
$$ \int _{ 0 }^{ \infty  }{ \dfrac { x\tan ^{ -1 }{ x }  }{ { (1+{ x }^{ 2 }) }^{ 2 } }  } dx$$ equals ?
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