3 Soal Integral, Poin Maks.

integral

86. ₁³∫ √(2x-2) dx = ₁³∫ (2x -2)¹/² dx

u = 2x - 2 --> du = 2 dx --> dx =  ¹/₂ du
batas integral
x = 1 --> u = 2(1) -2 = 0
x = 3 --> u = 2(3) - 2 = 4

= ₁³∫ √(2x-2) dx =₀⁴ ∫ ¹/₂ u¹/² du
= [¹/₃ u√u]⁴₀
= ¹/₃(4√4)
= 8/3

85. ₋₁² ∫ (2x+ 3x² + 4x³) dx
= [x² + x³ + x⁴]²₋₁
= (4-1) + (8+1) +(16-1)
= 27

86.₀¹ ∫ (dx) / (1 +x²) = [ tan⁻¹(x) ]¹₀ = tan⁻¹ (1) - tan⁻¹ (0) = π/4