Hitunglah nilai integral berikut.a. integral 4 8 2/3 x^5

Nilai integral a adalah 28672 dan nilai integral b adalah 4(√2 - 1).

Pembahasan

Berikut adalah perhitungan nilai integral:

a. ∫[4, 8] (2/3)x^5 dx
= (2/3) * ∫[4, 8] x^5 dx
= (2/3) * [x^6/6] |_[4, 8]
= (2/18) * [x^6] |_[4, 8]
= (1/9) * (8^6 - 4^6)
= (1/9) * (262144 - 4096)
= (1/9) * 258048
= 28672

b. ∫[1, 4] x^(-3/4) dx
= [x^(-3/4 + 1) / (-3/4 + 1)] |_[1, 4]
= [x^(1/4) / (1/4)] |_[1, 4]
= [4 * x^(1/4)] |_[1, 4]
= 4 * (4^(1/4) - 1^(1/4))
= 4 * (√2 - 1)