Mathematics

The value of $$\displaystyle \underset{0}{\overset{x}{\int}} \dfrac{(t - |t|)^2}{(1 + t^2)} dt$$ is equal to


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Q1 Single Correct Medium
If $$\displaystyle \frac{ax}{(x+2)(x-1)} = \frac{2}{x+2}+\frac{1}{x-1}$$, then a = 
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Asked in: Mathematics - Integrals


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The value of $$\displaystyle \lim_{n \rightarrow \infty} e^{\frac{3i}{n}} \cdot \dfrac{3}{n} = ?$$
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Q3 Subjective Medium
Evaluate the following integral
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Q4 Single Correct Medium
$$\displaystyle \int { \frac { \cos { x } +x\sin { x }  }{ x\left( x+\cos { x }  \right)  } dx } $$ is equal to 
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Let us consider the integral of the following forms
$$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$$
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Asked in: Mathematics - Integrals


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