3.7.4 Pengamiran, SPM Praktis (Kertas 1)

Soalan 8:

\begin{array}{l} Diberi \int_{- 2}^{3} g (x) d x = 4, dan \int_{- 2}^{3} h (x) d x = 9, cari nilai bagi \\ (a) \int_{- 2}^{3} 5 g (x) d x, \\ (b) m jika \int_{- 2}^{3} [g (x) + 3 h (x) + 4 m] d x = 12 \end{array}

Penyelesaian:
(a)

\begin{array}{l} \int_{- 2}^{3} 5 g (x) d x = 5 \int_{- 2}^{3} g (x) d x \\ = 5 \times 4 \\ = 20 \end{array}

(b)

\begin{array}{l} \int_{- 2}^{3} [g (x) + 3 h (x) + 4 m] d x = 12 \\ \int_{- 2}^{3} g (x) d x + 3 \int_{- 2}^{3} h (x) d x + \int_{- 2}^{3} 4 m d x = 12 \\ 4 + 3 (9) + 4 m {[x]}_{- 2}^{3} = 12 \\ 4 m [3 - (- 2)] = - 19 \\ 20 m = - 19 \\ m = - \frac{19}{20} \end{array}

Soalan 9:

Diberi y = \frac{5 x}{x^{2} + 1} dan \frac{d y}{d x} = g (x), cari nilai bagi \int_{0}^{3} 2 g (x) d x .

Penyelesaian:

\begin{array}{l} Memandangkan \frac{d y}{d x} = g (x), maka y = \int g (x) d x \\ \int_{0}^{3} 2 g (x) d x = 2 \int_{0}^{3} g (x) d x \\ = 2 {[y]}_{0}^{3} \\ = 2 {[\frac{5 x}{x^{2} + 1}]}_{0}^{3} \\ = 2 [\frac{5 (3)}{3^{2} + 1} - 0] \\ = 2 (\frac{15}{10}) \\ = 3 \end{array}

Soalan 10:

Cari \int_{5}^{k} (x + 1) d x, dalam sebutan k .

Penyelesaian:

\begin{array}{l} {\int_{5}^{k} (x + 1) d x = [\frac{x^{2}}{2} + x]}_{5}^{k} \\ = (\frac{k^{2}}{2} + k) - (\frac{5^{2}}{2} + 5) \\ = \frac{k^{2} + 2 k}{2} - \frac{35}{2} \\ = \frac{k^{2} + 2 k - 35}{2} \end{array}