English

Find Integral (Sin 2 X - Cos 2x)By(Sin X Cos X) Dx

Advertisements
Advertisements

Question

Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`

Advertisements

Solution

`int (sin^2 x - cos^2x)/(sin x cos x) dx`

= `int (sin^2 x)/(sin x cos x) dx - int (cos^2 x)/(sin x cos x) dx`

= `int tan x dx - int cot x dx`

= log |sec x| - log |sin x| + C

shaalaa.com
  Is there an error in this question or solution?
2016-2017 (March) All India Set 3

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate : `intsin(x-a)/sin(x+a)dx`

 


Find the integrals of the function:

sin3 x cos3 x


Find the integrals of the function:

sin x sin 2x sin 3x


Find the integrals of the function:

`(1-cosx)/(1 +  cos x)`


Find the integrals of the function:

`cos x/(1 + cos x)`


Find the integrals of the function:

`(sin^2 x)/(1 + cos x)`


Find the integrals of the function:

`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`


Find the integrals of the function:

tan4x


Find the integrals of the function:

sin−1 (cos x)


Find  `int dx/(x^2 + 4x + 8)`


Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx


Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`


Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .


Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .


Find `int_  (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `


Find `int_  sin ("x" - a)/(sin ("x" + a )) d"x"`


Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration. 


Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`


Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`


The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4  dx` is


Which identity is used for an even power of cosine?


Which identity is used for the product of sine and cosine?


Which identity is used for \(\sin^3 x\)?


Using \(\cos^2 x = \frac{1+\cos 2x}{2}\), which expression is equivalent to \(\int \cos^2 x\,dx\)?


What is \(\int \sin 2x\cos 3x\,dx\)?


Which procedure is recommended when an identity can simplify a complicated trigonometric expression?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×