Advertisements
Advertisements
प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Advertisements
उत्तर
`intsinx/sqrt(36-cos^2x)dx`
Substitute, cosx = t
∴ - sin x dx = dt
∴ sin x dx = - dt
The integral becomes
`int (-dt)/sqrt( 36 - t^2 )`
= `-intdt/sqrt( 6^2 - t^2 )`
= `-sin^-1( t/6 ) + C`
= `-sin^-1 .(cosx/6) + c`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`1/(1 + cot x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : sin5x.cos8x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: ∫ |x| dx if x < 0
`int (log x)/(log ex)^2` dx = _________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (cos x)/(1 - sin x) "dx" =` ______.
`int (logx)^2/x dx` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
