Advertisements
Advertisements
Question
Integrate the functions:
`sqrt(ax + b)`
Advertisements
Solution
Let `I = int sqrt(ax + b) dx`
Put ax + b = t
a dx = dt
`=> dx = 1/a dt`
Hence, `I = int 1/a sqrtt dt`
`= 1/a int t^(1/2) dt`
`= 1/a . 2/3 t^(3/2) + C`
`= 2/(3a) (ax + b)^(3/2) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :`intxlogxdx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int "x" * "e"^"2x"` dx
`int (log x)/(log ex)^2` dx = _________
`int sec^6 x tan x "d"x` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The value of `intsinx/(sinx - cosx)dx` equals ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
