Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Advertisements
उत्तर
Let I = `int sqrt((x - 3)(7 - x)).dx`
=`intsqrt(-x^2 + 10x - 21).dx`
= `int sqrt(- (x^2 - 10x + 21)).dx`
= `int sqrt(4 -(x^2 - 10x + 25)).dx`
= `int sqrt(2^2 - (x - 5)^2`
= `((x - 5)/2) sqrt(2^2 - (x - 5)^2) + 2^2/(2) sin^-1 ((x - 5)/2) + c`
= `((x - 5)/2) sqrt((x - 3)(7 - x)) + 2sin^-1 ((x - 5)/2) + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sin x.
Integrate the function in x (log x)2.
Integrate the function in e2x sin x.
`intx^2 e^(x^3) dx` equals:
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Integrate the following w.r.t.x : log (log x)+(log x)–2
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/("9x"^2 - 25)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int ("d"x)/(x - x^2)` = ______
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int logx/(1 + logx)^2 "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
`intsqrt(1+x) dx` = ______
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
