Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Advertisements
उत्तर
Let I = `int x/ (sqrt( x + 4)) dx`
Put x + 4 = t
⇒ dx = dt . Also, x = t - 4
∴ `I = int (t - 4)/sqrtt dt`
`= int (t^(1/2) - 4t^ (-1/2)) dt`
`= 2/3 t^(3/2) -4 xx 2t^(1/2) + C`
`= 2/3 (x + 4)^(3/2) - 8 (x + 4)^(1/2) + C`
`= 2/3 (x + 4)^(1/2) [x + 4 - 12] + C`
`= 2/3 (x + 4)^(1/2) (x - 8) + C`
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following : `int (logx)2.dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
`int x^3"e"^(x^2) "d"x`
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int (logx)^2/x dx` = ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
