Evaluate-4-5-2-ln-x-dx-using-trapezoidal-rule-take-h-0-2-

Question Number 9623 by tawakalitu last updated on 21/Dec/16

Evaluate : \int_{4}^{5.2} \ln (x) dx

using trapezoidal rule . take h = 0.2

Commented by sandy_suhendra last updated on 21/Dec/16

Answered by sandy_suhendra last updated on 21/Dec/16

\int_{4}^{5.2} \ln x dx

\approx \frac{Δ x}{2} [f (4) + 2 f (4.2) + 2 f (4.4) + \dots + 2 f (5) + f (5.2)]

\approx \frac{0.2}{2} [\ln 4 + 2 \ln 4 . 2 + \dots + 2 \ln 5 + \ln 5 . 2]

\approx 0.1 \ln [4 \times 4 . 2^{2} \times 4 . 4^{2} \times 4 . 6^{2} \times 4 . 8^{2} \times 5^{2} \times 5.2]

\approx 0.1 \times 18.24 (I use calculator)

\approx 1.824

Commented by tawakalitu last updated on 21/Dec/16

i really appreciate your effort sir . God bless

you .