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 `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`e^(2x+3)`
Write a value of
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
`int cot^2x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int 1/(sinx.cos^2x)dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x-1))dx`
