Advertisements
Advertisements
प्रश्न
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Advertisements
उत्तर
According to question,
let I = `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
I = `int_ (sin "x" - cos "x")/sqrt(sin^2 "x" + cos^2 "x" + 2 sin "x" .cos "x") d"x"`
= `int_ ( sin "x" - cos "x")/sqrt((sin"x" + cos "x")^2 d"x"`
= `int_ (sin "x" - cos "x")/(sin "x" + cos "x") d"x"`
let sin x + cos x = t
⇒ (cos x - sin x) dx = dt
I = `int_ (-1)/("t") d"t"`
= -ln t + C
= ln `(1/"t") + "C"`
⇒ I = ln `((1)/(sin "x" + cos "x")) + "C"`
APPEARS IN
संबंधित प्रश्न
Find the integrals of the function:
sin2 (2x + 5)
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:
cos4 2x
Find the integrals of the function:
tan4x
Find the integrals of the function:
sin−1 (cos x)
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
Which identity is used for \(\cos^2 x\)?
What is \(\int \cos^2 x\,dx\)?
Which procedure is recommended when an identity can simplify a complicated trigonometric expression?
After a trigonometric expression has been simplified, how should it be integrated?
