**Soalan 8:**$\begin{array}{l}\text{Diberi}{\displaystyle {\int}_{-2}^{3}g(x)dx=4},\text{dan}{\displaystyle {\int}_{-2}^{3}h(x)dx=9}\text{,carinilaibagi}\\ \text{(a)}{\displaystyle {\int}_{-2}^{3}5g(x)dx,}\\ \text{(b)}m\text{jika}{\displaystyle {\int}_{-2}^{3}\left[g(x)+3h\left(x\right)+4m\right]dx=12}\end{array}$

*Penyelesaian*:**(a)**

$\begin{array}{l}{\displaystyle {\int}_{-2}^{3}5g(x)dx=5}{\displaystyle {\int}_{-2}^{3}g(x)dx}\\ \text{}=5\times 4\\ \text{}=20\end{array}$

**(b)**

$\begin{array}{l}{\displaystyle {\int}_{-2}^{3}\left[g(x)+3h\left(x\right)+4m\right]dx=12}\\ {\displaystyle {\int}_{-2}^{3}g(x)dx+3}{\displaystyle {\int}_{-2}^{3}h\left(x\right)dx+}{\displaystyle {\int}_{-2}^{3}4mdx=12}\\ 4+3\left(9\right)+4m{\left[x\right]}_{-2}^{3}=12\\ \text{}4m\left[3-\left(-2\right)\right]=-19\\ \text{}20m=-19\\ \text{}m=-\frac{19}{20}\end{array}$

**Soalan 9:**

$\text{Diberi}y=\frac{5x}{{x}^{2}+1}\text{dan}\frac{dy}{dx}=g\left(x\right),\text{carinilaibagi}{\displaystyle {\int}_{0}^{3}2g\left(x\right)dx.}$

*Penyelesaian*:$\begin{array}{l}\text{Memandangkan}\frac{dy}{dx}=g\left(x\right),\text{maka}y={\displaystyle \int g\left(x\right)}dx\\ {\displaystyle {\int}_{0}^{3}2g\left(x\right)dx=2{\displaystyle {\int}_{0}^{3}g\left(x\right)dx}}\\ \text{}=2{\left[y\right]}_{0}^{3}\\ \text{}=2{\left[\frac{5x}{{x}^{2}+1}\right]}_{0}^{3}\\ \text{}=2\left[\frac{5\left(3\right)}{{3}^{2}+1}-0\right]\\ \text{}=2\left(\frac{15}{10}\right)\\ \text{}=3\end{array}$

**Soalan 10:**

$\text{Cari}{\displaystyle {\int}_{5}^{k}\left(x+1\right)dx,\text{dalamsebutan}k.}$

*Penyelesaian*:$\begin{array}{l}{{\displaystyle {\int}_{5}^{k}\left(x+1\right)dx=\left[\frac{{x}^{2}}{2}+x\right]}}_{5}^{k}\\ \text{}=\left(\frac{{k}^{2}}{2}+k\right)-\left(\frac{{5}^{2}}{2}+5\right)\\ \text{}=\frac{{k}^{2}+2k}{2}-\frac{35}{2}\\ \text{}=\frac{{k}^{2}+2k-35}{2}\end{array}$