Mathematics

# Evaluate the following definite integral:$\displaystyle \int_{1}^{2} e^{2x} \left (\dfrac {1}{x}-\dfrac {1}{2x^2}\right)dx$

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

#### Realted Questions

Q1 Single Correct Medium
Match the following with I, II, III
If $\displaystyle \frac{x^{2}-x+3}{x^{3}-1}=\frac{A}{(x-1)}+\frac{Bx+C}{(x^{2}+x+1)}$ then

I) $A=$             a)  0
II) $B=$            b)  1
III) $C=$          c)  -2
• A. a, b, c
• B. b, c, a
• C. a, c,b
• D. b, a, c

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int \frac{\sin 2x}{1+\sin ^{2}x}dx.$
• A. $\displaystyle \log \left ( 1-\sin ^{2}x \right ).$
• B. $\displaystyle \log \left ( 1+\cos ^{2}x \right ).$
• C. $\displaystyle \log \left ( 1-\cos ^{2}x \right ).$
• D. $\displaystyle \log \left ( 1+\sin ^{2}x \right ).$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate:
$\int _{ 0 }^{ \pi }{ \dfrac { dx }{ 5+3cosx } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle \lim_{n \rightarrow \infty} \displaystyle \Sigma_{i=1}^{n-1} \sqrt{4 +\dfrac{5i}{n}}$ is equal to?
• A. $15/38$
• B. $21/15$
• C. $22/15$
• D. $38/15$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$