Mathematics

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


SOLUTION

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

$$I=\left [2\log x \right]_1^2$$ 

$$I=2\log 2-2\log 1$$ 

$$I=2\log 2 $$

View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle \frac{1}{4\sqrt{2}}ln \left | \frac{1\, +\, \sqrt{2}sin\, x}{1\, -\, \sqrt{2}sin\, x} \right |\, -\, \frac{1}{8}ln \left | \frac{1\, +\, sin\, x}{1\, -\, sin\, x} \right |\, +\, c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$ - cot x -x + C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Find $$\int {\sin \left( {ax + b} \right)\cos \left( {ax + b} \right)dx} $$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer