definite integral hirap po talaga hindi ko masagot

img_20160208_1552001.jpg

1/30dx(49x2)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(49x2)2

      =π/6023cosθdθ[22(2sinθ)2]2

      =124π/60cosθdθ(1sin2θ)2

      =124π/60cosθdθcos4θ

      =124π/60dθcos3θ

      =124π/60sec3θdθ

For

sec3θdθ

Let
u = sec θ
du = sec θ tan θ dθ

dv = sec2 θ dθ
v = tan θ
 

sec3θdθ

      =secθtanθtanθ(secθtanθ)dθ

      =secθtanθtan2θsecθdθ

      =secθtanθ(sec2θ1)secθdθ

      =secθtanθsec3θdθ+secθdθ

2sec3θdθ=secθtanθ+secθdθ

2sec3θdθ=secθtanθ+ln(secθ+tanθ)

sec3θdθ=12secθtanθ+12ln(secθ+tanθ)

 

Hence,
1/30dx(49x2)2

      =124π/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[23(33)+ln(23+33)]148[1(0)+ln(1+0)]

      =148[23+ln(3)]

      =0.0253