Advertisements
Advertisements
प्रश्न
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
पर्याय
`"e"^x cos x + "C"`
`"e"^x sin x + "C"`
`-"e"^x cos x + "C"`
`-"e"^x sin x + "C"`
उत्तर
`int "e"^x (cosx - sinx)"d"x` is equal to `"e"^x cos x + "C"`.
Explanation:
`int "e"^x ["f"(x) + "f"(x)]"d"x = "e"^x "f"(x) + "C"`.
Here f(x) = cosx, f'(x) = `- sin x`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
tan3 2x sec 2x
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Evaluate `int_0^(3/2) |x sin pix|dx`
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int x^2tan^-1x"d"x`
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
`int sinx/(3 + 4cos^2x) "d"x` = ______.
