Advertisements
Advertisements
प्रश्न
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Advertisements
उत्तर
Let I = `int (x - 2)^2 sqrt(x)*dx`
= `int (x^2 - 4x + 4)sqrt(x)*dx`
= `int (x^(5/2) - 4x^(3/2) + 4x^(1/2))*dx`
= `int x^(5/2)*dx - 4 int x^(3/2)*dx + 4 int x^(1/2)*dx`
= `x^(7/2)/((7/2)) - 4 x^(5/2)/((5/2)) + 4 x^(3/2)/((3/2))`
= `(2)/(7)x^(7/2) - 8/5x^(5/2) + (8)/(3)x^(3/2) + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int log ("x"^2 + "x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 1/(cos x - sin x)` dx = _______________
`int 1/(xsin^2(logx)) "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int1/(x(x-1))dx`
