-dxsin x-asin x-b is equal towhere a b and C is constant of integration

Let I=∫dxsin (x a)sin (x b) ⇒ I= 1sin (b a)∫sin ((x a) (x b))dxsin (x a)sin (x b) ⇒ I=cosec (b a)[ ∫ (x b)dx nbsp;∫ (x a) dx] ⇒ I=cosec (b a)[ ln |sin(x b) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sin(A+B)Sin(A-B)

∫dxsin x-asin...

Question

$\int \frac{d x}{sin (x - a) sin (x - b)}$ is equal to
(where $a \neq b$ and $C$ is constant of integration)

sin (b - a) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

cosec (b - a) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

cosec (a - b) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sin (a - b) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $cosec (b - a) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C$
Let
$I = \int \frac{d x}{sin (x - a) sin (x - b)}$
$\Rightarrow I = \frac{1}{sin (b - a)} \int \frac{sin ((x - a) - (x - b)) d x}{sin (x - a) sin (x - b)}$
$\Rightarrow I = cosec (b - a) [\int cot (x - b) d x - \int cot (x - a) d x]$
$\Rightarrow I = cosec (b - a) [ln | sin (x - b) | - ln | sin (x - a) |] + C$
$∴ I = cosec (b - a) ln ∣ ∣ ∣ \frac{sin (x - b)}{sin (x - a)} ∣ ∣ ∣ + C$

Suggest Corrections

Similar questions

\int (1 - x) \sqrt{x} d x

is equal to(where

C

is constant of integration)

\int \sqrt{sec x - 1} d x

is equal to
(where

C

is integration constant)

Q. If

\int \frac{\sqrt{x}}{x + 1} d x = A \sqrt{x} + B {tan}^{- 1} \sqrt{x} + C,

then

| A | + | B |

is equal to
(where

C

is integration constant and

A

and

B

are fixed constants)

\int \frac{d x}{1 + e^{- x}}

is equal to
where c is the constant of integration

Q. What is

\int \frac{x e^{x} d x}{(x + 1)^{2}}

equal to?
where

c

is the constant of integration.

Join BYJU'S Learning Program

Explore more

Sin(A+B)Sin(A-B)

Standard XII Mathematics

Join BYJU'S Learning Program

∫dxsin(x−a)sin(x−b) is equal to (where a≠b and C is constant of integration)

$\int \frac{d x}{sin (x - a) sin (x - b)}$ is equal to
(where $a \neq b$ and $C$ is constant of integration)