Advertisements
Advertisements
Question
Find the integrals of the function:
sin−1 (cos x)
Advertisements
Solution
Let `I - int sin^-1 (cos x) dx`
`int sin^-1 [sin (pi/2 - x)] dx`
`= int (pi/2 - x) dx`
`= pi/2 int dx - int x dx`
`= (pix)/2 - x^2/2 +C`
APPEARS IN
RELATED QUESTIONS
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
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:
sin3 x cos3 x
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
tan4x
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int dx/(x^2 + 4x + 8)`
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 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.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
What does integration using trigonometric identities mean?
Which identity is used for \(\cos^2 x\)?
Which identity is used for an even power of cosine?
Which identity is used for \(\sin^3 x\)?
What is \(\int \sin 2x\cos 3x\,dx\)?
After a trigonometric expression has been simplified, how should it be integrated?
What must always be added to an indefinite integral?
