Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
पर्याय
`x cot (x/2) + c`
`- x cot (x/2) + c`
`cot (x/2) + c`
`x tan (x/2) + c`
Advertisements
उत्तर
`- x cot (x/2) + c`
[ Hint : `int (x- sinx)/(1 - cosx)*dx = int (x - 2sin(x/2)cos(x/2))/(2sin^2 (x/2))*dx`
= `(1)/(2) int x"cosec"^2(x/2)*dx - int cot(x/2)*dx`
= `(1)/(2) [x int "cosec"^2 (x/2)*dx - int [d/dx(x) int "cosec"^2(x/2)^(dx)]*dx - int cot(x/2)*dx`
= `(1)/(2)[x{(-cot(x/2))/((1/2))} - int1* (-cot(x/2))/((1/2))*dx - intcot(x/2)*dx`
= `xcot(x/2) + int cot(x/2)*dx - int cot(x/2)*dx`
= `- x cot(x/2) + c`].
APPEARS IN
संबंधित प्रश्न
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Integrate the function in x sin 3x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in x (log x)2.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^2.log x.dx`
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int log(logx)/x.dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int (cos2x)/(sin^2x cos^2x) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Solve: `int sqrt(4x^2 + 5)dx`
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Evaluate `int(1 + x + (x^2)/(2!))dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
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)
Evaluate:
`int x^2 cos x dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Which function is an example under priority \(I\) in the LIATE rule?
Which pair is listed as Exponential in the LIATE rule?
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
