KUIS (medium-hard)
[tex]\begin{aligned} \tt Jika &= \tt \sqrt{a^2-x^2} \\ \tt x &= \tt a~sin(\theta)\\ \tt Tentukan &~~ \tt hasil~~dari\\&\int _{5\sqrt{2}}^{10}2\sqrt{100-x^2}~~dx\end{aligned}[/tex]
[tex]\begin{aligned} \tt Jika &= \tt \sqrt{a^2-x^2} \\ \tt x &= \tt a~sin(\theta)\\ \tt Tentukan &~~ \tt hasil~~dari\\&\int _{5\sqrt{2}}^{10}2\sqrt{100-x^2}~~dx\end{aligned}[/tex]
Jawab:
Penjelasan dengan langkah-langkah:
x = a sin(t)
x/a = sin(t)
sin^-1(x/a) = t
= integral akar(a^2 - x^2)
= x/2 akar(a^2 - x^2) + a^2/2 x sin^-1(x/a) + c
= x/2 akar(100 - x^2) + 100/2 x t
= x/2 akar(100 - x^2) + 50t [5 akar2 to 10]
= [10/2 x akar(100 - 10^2) + 50t] - [5 akar2 /2 x akar(100 - (5 akar2)^2) + 50t]
= [0 + 50t] - [2.5 akar2 x akar(100 - 50) + 50t]
= - 2.5 akar2 x akar50
= -2.5 akar2 x akar2 x 5
= -2.5 x 2 x 5
= -25