Advertisements
Advertisements
प्रश्न
Evaluate the following integrals: `int sin 4x cos 3x dx`
Advertisements
उत्तर
`int sin 4x cos 3x dx`
= `(1)/(2)int sin 4x cos 3x dx` ...[∴ 2sinA.cosB = sin (A + B) + sin(A - B)]
= `(1)/(2)int [sin (4x + 3x) + sin (4x - 3x)]dx`
= `(1)/(2) int sin 7x dx + (1)/(2)int sin x dx`
= `(-1)/(2)((cos 7x)/7) + ((-1)/(2))cos x + c`
= `-(1)/(14)cos 7x - (1)/(2) cos x + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
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)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).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`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
`int sqrt(1 + "x"^2) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int(log(logx))/x "d"x`
`int sin^-1 x`dx = ?
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int (cos x)/(1 - sin x) "dx" =` ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
