Question

Integral part 1&2, jelaskan dgn caranya

Answer 1

Verified answer

Integral Substitusi
34. ∫ x  √(x² -5) dx
u = x² - 5
du = 2x dx
x dx = 1/2 du
∫ x√(x² -5) dx = ∫ 1/2 √u  du= 1/2 ∫ u^(1/2) du
= 1/2 (2/3) (U)^(3/2) + c
= 1/3 u√u + c
= 1/3 (x² - 5) √(x² -5) +C
.

35. ∫sin³ x . cos  x dx =
misl u =  sin x
du = cos x dx

∫ sin³ x  cos x dx = ∫ (sin x)³ (cos x dx) = ∫ u³ du = 1/4 u⁴ + c
= 1/4 ( sin x)⁴ + c
= 1/4 sin⁴ x + c.