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

Pertanyaan

Hitunglah nilai integral berikut: a. integral 4 8 2/3 x^5 dx b. integral 1 4 x^(-3/4) dx

Solusi

Verified

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)

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Topik: Integral
Section: Integral Tentu

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