Advertisements
Advertisements
प्रश्न
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Advertisements
उत्तर
Let `I = int sqrtsin 2x cos 2x dx`
Put sin 2x = t
⇒ 2 cos 2x dx = dt
∴ `I = 1/2 int t^(1/2) dt = 1/2 * t^(1/2 + 1)/(1/2 + 1) + C`
`1/2 xx 2/3 t^(3/2) + C = 1/2 t^(3/2) + C`
`1/3 (sin 2x)^(3/2) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
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 secx/(secx - tanx)dx` equals ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
`int 1/(sin^2x cos^2x)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(5x^2-6x+3)/(2x-3)dx`
