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Re: definite integral hirap po talaga hindi ko masagot
∫1/30dx(4−9x2)2
=∫1/30dx[22−(3x)2]2
Let
3x = 2 sin θ
3 dx = 2 cos θ dθ
dx = (2/3) cos θ dθ
When
x = 0, θ = 0,
x = 1/3, θ = 30° = π/6
Hence,
∫1/30dx(4−9x2)2
=∫π/6023cosθdθ[22−(2sinθ)2]2
=124∫π/60cosθdθ(1−sin2θ)2
=124∫π/60cosθdθcos4θ
=124∫π/60dθcos3θ
=124∫π/60sec3θdθ
For
Let
u = sec θ
du = sec θ tan θ dθ
dv = sec2 θ dθ
v = tan θ
∫sec3θdθ
=secθtanθ−∫tanθ(secθtanθ)dθ
=secθtanθ−∫tan2θsecθdθ
=secθtanθ−∫(sec2θ−1)secθdθ
=secθtanθ−∫sec3θdθ+∫secθdθ
2∫sec3θdθ=secθtanθ+∫secθdθ
2∫sec3θdθ=secθtanθ+ln(secθ+tanθ)
∫sec3θdθ=12secθtanθ+12ln(secθ+tanθ)
Hence,
∫1/30dx(4−9x2)2
=124∫π/60sec3θdθ
=124[12secθtanθ+12ln(secθ+tanθ)]π/60
=148[secθtanθ+ln(secθ+tanθ)]π/60
=148[secπ6tanπ6+ln(secπ6+tanπ6)] −148[sec0tan0+ln(sec0+tan0)]
=148[2√3(√33)+ln(2√3+√33)]−148[1(0)+ln(1+0)]
=148[23+ln(√3)]
=0.0253
Re: definite integral hirap po talaga hindi ko masagot
In reply to Re: definite integral hirap po talaga hindi ko masagot by Jhun Vert
thank you po talaga.atsaka bakit po pala naging pie over 6?
Re: definite integral hirap po talaga hindi ko masagot
In reply to Re: definite integral hirap po talaga hindi ko masagot by Jeanvill Palad…
Multiply by π/180 to convert degree to radian:
30∘=30∘×π180∘=π6 rad
pwd muh rin e direct sa
pwd muh rin e direct sa calculator pra m check muh ang sagot muh pg tama