Mathematics

# The value of the integral $\displaystyle \int_0^{2 \pi} \frac{sin 2 \theta}{a - b cos \theta} d \theta$ when a > b > 0, is

##### SOLUTION
Let $I=\int _{ 0 }^{ 2\pi }{ \cfrac { sin2\theta }{ a-bcos\theta } d\theta }$   ...(1)
Using property $\int _{ 0 }^{ a }{ f\left( x \right) dx } =\int _{ 0 }^{ a }{ f\left( a-x \right) dx }$
$I=\int _{ 0 }^{ 2\pi }{ \cfrac { sin2\left( 2\pi -\theta \right) }{ a-bcos\left( 2\pi -\theta \right) } d\theta } =\int _{ 0 }^{ 2\pi }{ \cfrac { sin\left( 4\pi -2\theta \right) }{ a-bcos\theta } d\theta }$
$=-\int _{ 0 }^{ 2\pi }{ \cfrac { sin2\theta }{ a-bcos\theta } d\theta }$   ...(2)
$2I=0\Rightarrow I=0$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Hard
$\displaystyle\int { \dfrac { \sin { x } }{ \sin { x } -\cos { x } } } dx=$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\int _0^1 xdx = \dfrac {\pi}{4} - \dfrac {1}{2} ln 2$ then the value of definite integral $\int _0^1 \tan^{-1} (1-x+x^2) dx$ equals :
• A. $\dfrac {\pi}{4} + ln 2$
• B. $\dfrac {\pi}{4} - ln2$
• C. $2 ln 2$
• D. $ln2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate:
$\int {\dfrac{{5x + 3}}{{\sqrt {{x^2} + 4x + 10} }}dx}$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve: $\displaystyle\int { \frac { 1 }{ \sqrt { x+a } } dx }$

Solve$\displaystyle \int_0^1 \dfrac{x^2-2}{x^2+1}dx$