Advertisements
Advertisements
प्रश्न
Find : `int(x+3)sqrt(3-4x-x^2dx)`
उत्तर
`I=int(x+3)sqrt(3-4x-x^2)dx`
Let (x+3)= `Ad/dx(3-4x-x^2)+B `
⇒ x+3=A(-2x-4)+B
⇒ x+3 = -2Ax-4A +B
∴ -2A=1
⇒A =`1/2`
-4A+B=3
⇒ `-4(-1/2)+B=3`
⇒ B =1
`:.I=int[-1/2d/dx(3-4x-x^2)+1]sqrt(3-4x-x^2dx)`
`=1/2intd/dx(3-4x-x^2)sqrt(3-4x-x^2)dx+intsqrt(3-4x-x^2-4+4)dx`
`=1/2((3-4x-x^2)^(3/2)/(3/2))+intsqrt(7-(x+2)^2)dx`
`=(3-4x-x^2)^(3/2)/3+(x+2)/2sqrt(7-(x+2)^2)+7/2sin^(-1)((x+2)/sqrt7)+C`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin (ax + b) cos (ax + b)
Write a value of
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int cos^2x.dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
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`.
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(1 + sin2x) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int cos^7 x "d"x`
`int x^3"e"^(x^2) "d"x`
`int dx/(1 + e^-x)` = ______
`int(5x + 2)/(3x - 4) dx` = ______
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
