Advertisements
Advertisements
प्रश्न
`int sin4x cos3x "d"x`
Advertisements
उत्तर
Let I = `int sin 4x * cos3x "d"x`
= `1/2 int (2 sin 4x * cos 3x) "d"x`
= `1/2 int [sin (4x + 3x) + sin(4x - 3x)] "d"x` .......[∵ 2 sin A cos B = sin(A + B) + sin(A − B)]
= `1/2 int (sin 7x + sin x) "d"x`
= `1/2 [int sin7 x "d"x + int sin x "d"x]`
= `1/2((-cos7x)/7 - cos x) + "c"`
∴ I = `- 1/14 cos 7x - 1/2 cos x + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x cos-1 x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `e^x (1/x - 1/x^2)`.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : log (x2 + 1)
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int (sinx)/(1 + sin x) "d"x`
`int ("d"x)/(x - x^2)` = ______
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x log x) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
∫ log x · (log x + 2) dx = ?
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int log x * [log ("e"x)]^-2` dx = ?
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int1/sqrt(x^2 - a^2) dx` = ______
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Solve the following
`int_0^1 e^(x^2) x^3 dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate `int tan^-1x dx`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
