Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Advertisements
उत्तर
Let I = `int(5 - 3x)(2 - 3x)^(-1/2).dx`
Put 2 – 3x = t
∴ –3dx = dt
∴ dx = `(-dt)/(3)`
Also, x = `(2 - t)/(3)`
∴ I = `int[5 - 3((2 - t)/3)]t^(-1/2).((-dt)/(3))`
= `-1/3(5 - 2 + t)t^(-1/2)dt`
= `-1/3 int(3 + t)t^(-1/2) dt`
= `-1/3 int(3t^(-1/2) + t^(1/2))dt`
= `-3/3 int t^(-1/2)dt - (1)/(3) int t^(1/2) dt`
= `-t^(1/2)/((1/2)) - (1)/(3).t^(3/2)/((3/2)) + c`
= `-2sqrt(2 - 3x) - (2)/(9)(2 - 3x)^(3/2) + c`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
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
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 sqrt(x^2 - 8x + 7)` dx
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int logx/x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int cot^2x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
`int secx/(secx - tanx)dx` equals ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
