Pengamiran ( Soalan Dan Jawapan )
1. Kamilkan
setiap yang berikut : a)
∫ x2 dx =
x2 / 3 + c b)
∫ x3 dx =
x4 / 4 + c c)
∫ (3x2 + 2x) dx = x3 + x2 +
c d)
∫ ( 2x2 + 3x – 1) dx = 2x3 /3 +3x2
/ 2 – x + c e)
∫ ( 4x3 – x 2) dx = x4 –
x3 / 3 + c f)
∫ ( x + 1/x ) dx = ∫ x dx + ∫1/x dx = x2
/ 2 + ln x + c g)
∫ ( 2/x ) dx = 2 ∫ 1/x dx = 2 ln x + c h)
∫ x2/3 dx = x5/3 / 5/3
+ c = 3x5/3 /5 + c i)
∫ x2 ( x-1 ) dx = ∫ ( x3 – x 2)
dx = x4 / 4 – x3 / 3 + c j)
∫ ( 1 – 3x ) (1 – x ) dx =
∫ ( 1 – 4x + 3x2 ) dx = x – 2x2 + x3
+ c k)
∫ ( x3 +
1 ) / x2 dx = ∫ ( x + x -2) dx = x2
/ 2 – 1 / x + c l) ∫ ( x – 1 ) / x dx = ∫ ( 1 – 1/x ) dx = x – ln x + c |
|
2. Kamirkan
bagi setiap fungsi tertentu a) Katakan a = sin x Da / dx = kos x Dx = da / kos x ∫ sin2 x . kos x dx = ∫ a2 kos x da / kos x = a3 / 3 + c = sin3 / 3 + c b) Katakan x / 2 = a Da / dx = ½ Dx = 2 da ∫ sin ( x/2 ) dx = ∫ sin a 2 da = 2 ∫ sin a da = 2 ( - kos a ) + c = - 2 kos ( x/2 ) + c c) Katakan a = 3x Da / dx = 3 Dx = da / 3 ∫ kos 3x dx = ∫ kos a da/3 = 1/3 ∫ kos a da = 1/3 ( sin a ) + c = 1/3 sin 3x + c d) Katakan a = 2x – 3 Da /dx = 2 Dx = da / 2 ∫ dx / ( 2x – 3 ) = ∫ da / 2 / a = ½ ∫ da /a = ½ ln a + c =
½ ln ( 2x + c ) + c |
e) Katakan a = x2 - 1 Da /dx = 2x Dx = da / 2x ∫ x / ( x2 - 1 ) dx = ∫ x /a da/2x = ½ ∫ 1/a da = ½ ln ( x2 - 1 ) + c f) Katakan a = x3 – 4 Da / dx = 3x2 Dx = da / 3x2 ∫ 2x2 / ( x3 – 4 ) dx =
∫ 2x2 / a a / 3x2 = 2/3 ∫ 1/a a = 2/3 ln a + c = 2/3 in ( x3 – 4 ) + c g) Katakan a = kos x Da / dx = - sin x Dx = da / - sin x ∫ tan x dx = ∫ sin x / kos x dx = ∫ sin x / a . da / - sin x = -1 ∫ 1/a da = -1 ln a + c = -1 ln cos x + c h) Katakan a = 3x Da / dx = 3 Dx = da / 3 ∫ e3x dx = ∫ ea da/3 = 1/3 ∫ ea da = 1/3 ea + c = e3x / 3 + c |