Mathematics

The integral $$\displaystyle \int_2^4\frac {log x^2}{log x^2+log (36-12x+x^2)}dx$$ is equal to


ANSWER

$$1$$


SOLUTION
$$I = \displaystyle \int_2^4 { \dfrac{2 log x } { 2 log x + 2 log (6-x) } } dx$$

$$I = \displaystyle \int_2^4{ \dfrac{log x}{ log x + log (6-x)} }dx$$

Using the property $$\displaystyle \int_{a}^b f(x) \ dx= \int _{a}^{b} f(a+b-x) \ dx$$
 we get, 

$$I = \displaystyle \int_2^4{\dfrac{log (6-x)}{log x + log (6-x)} }dx$$

Adding the two integrals we get, 

$$2 I = \displaystyle \int_2^4 {1}{dx}$$

Hence, $$2I = 2 $$

Hence, $$I =1 $$
View Full Answer

Its FREE, you're just one step away


Single Correct Hard Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Solve : $$\underset{0}{\overset{\frac{\pi}{2}}{\int}} \tan^5 x \cos^8 \, x \, dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate the following integral
$$\int { \cfrac { \cos { 2x } +x+1 }{ { x }^{ 2 }+\sin { 2x } +2x }  } dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Integrate:
$$\displaystyle \int{\dfrac{\sqrt{1-x^{2}}+\sqrt{1+x^{2}}}{\sqrt{1-x^{4}}}}dx=$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int{\tan^2x}dx$$
  • A. $$\tan x+c$$
  • B. $$\tan x-x$$
  • C. None of the above
  • D. $$\tan x-x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int \frac{2x^{2}}{3x^{4}2x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer