Mathematics

# Evaluate: $\displaystyle\int_{1}^{2} \dfrac 2x\ dx$

##### SOLUTION

consider, $I=\displaystyle\int_{1}^{2} \dfrac 2x\ dx$

$I=\left [2\log x \right]_1^2$

$I=2\log 2-2\log 1$

$I=2\log 2$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Solve:
$\displaystyle\int {\dfrac{{4x + 6}}{{2{x^2} + 5x + 3}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
Evaluate:$\displaystyle \int \frac{dx}{\sqrt{2+2x-x^{2}}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate : $\displaystyle \int \frac{sin\, x}{sin\, 4x}$dx
• A. $\displaystyle \frac{1}{2\sqrt{2}}ln \left | \frac{1\, +\, \sqrt{2}sin\, x}{1\, -\, \sqrt{2}sin\, x} \right |\, +\, \frac{1}{8}ln \left | \frac{1\, +\, sin\, x}{1\, -\, sin\, x} \right |\, +\, c$
• B. $\displaystyle \frac{1}{2\sqrt{2}}ln \left | \frac{1\, +\, \sqrt{2}sin\, x}{1\, -\, \sqrt{2}sin\, x} \right |\, -\, \frac{1}{8}ln \left | \frac{1\, +\, sin\, x}{1\, -\, sin\, x} \right |\, +\, c$
• C. $\displaystyle \frac{1}{4\sqrt{2}}ln \left | \frac{1\, +\, \sqrt{2}sin\, x}{1\, -\, \sqrt{2}sin\, x} \right |\, +\, \frac{1}{8}ln \left | \frac{1\, +\, sin\, x}{1\, -\, sin\, x} \right |\, +\, c$
• D. $\displaystyle \frac{1}{4\sqrt{2}}ln \left | \frac{1\, +\, \sqrt{2}sin\, x}{1\, -\, \sqrt{2}sin\, x} \right |\, -\, \frac{1}{8}ln \left | \frac{1\, +\, sin\, x}{1\, -\, sin\, x} \right |\, +\, c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate : $\displaystyle \int cot^2 x dx$
• A. $cot x -x + C$
• B. $-cot x+ x +C$
• C. $cot x + x +C$
• D. $- cot x -x + C$

Find $\int {\sin \left( {ax + b} \right)\cos \left( {ax + b} \right)dx}$.