Advertisements
Advertisements
प्रश्न
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Advertisements
उत्तर
Let I = `int_ sin("x" - a)/sin ("x" + a)d"x"`
⇒ I = `int_ sin [("x" + a) - 2a]/sin ("x" + a)d"x"`
= `int_ (sin ("x" + a )·cos (2a) - cos ("x" + a)· sin (2a))/sin ("x" + a)d"x"`
= `int_ cos (2a) d"x" - int_ cot ("x" + a)· sin (2a)d"x"`
= x·cos (2a) - log|sin (x + a)|·sin (2a) + C
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin4 x
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
sin−1 (cos x)
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
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 the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Find `int x^2tan^-1x"d"x`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
Which identity is used for \(\cos^2 x\)?
Which identity is used for the product of sine and cosine?
What is \(\int \cos^2 x\,dx\)?
Applying the product-to-sum identity to \(\sin 2x\cos 3x\) gives which expression?
What should be done first when evaluating an integral containing a complicated trigonometric expression?
Which procedure is recommended when an identity can simplify a complicated trigonometric expression?
