Sifat-sifat Integral Tentu - Latihan Soal

Diberikan nilai dari tiga buah integral tentu sebagai berikut:

\(\begin{align}\mathrm{\int_{0}^{2}f(x)dx=3\,\int_{2}^{0}g(x)dx=4,}\end{align}\) dan \(\begin{align}\mathrm{\int_{0}^{2}h(x)dx=5}\end{align}\)

Tentukan nilai dari:

\(\begin{align}\mathrm{\int_{0}^{2}[f(x)+g(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[g(x)+h(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[f(x)-h(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[h(x)-g(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[f(x)+g(x)-h(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[2f(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}[-5g(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}\left [\frac{1}{10}h(x)\right ]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{2\int_{0}^{2}[15g(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{-\frac{1}{3}\int_{0}^{2}[-21h(x)]dx=\,...}\end{align}\)

Diberikan nilai dari tiga buah integral tentu sebagai berikut:

\(\begin{align}\mathrm{\int_{-1}^{1}f(t)dt=10,\,\int_{-1}^{1}g(t)dt=20,}\end{align}\) dan \(\begin{align}\mathrm{\int_{-1}^{1}h(t)dt=30}\end{align}\)

Tentukan nilai dari:

\(\begin{align}\mathrm{\int_{-1}^{1}[2f(t)+3g(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[5g(t)+7h(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[f(t)-4g(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[3h(t)-2f(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[5f(t)+7g(t)+11h(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[g(t)+6f(t)-8h(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[6h(t)-7f(t)+4g(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{1}[2h(t)-5g(t)-8f(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\frac{1}{10}\int_{-1}^{1}[4f(t)-2g(t)+3h(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{-\frac{1}{5}\int_{-1}^{1}[-10g(t)+20h(t)-30f(t)]dt=\,...}\end{align}\)

Diberikan nilai dari empat buah integral tentu sebagai berikut:

\(\begin{align}\mathrm{\int_{0}^{1}f(x)dx=1,\,\int_{1}^{2}f(x)dx=2,\int_{0}^{1}g(x)dx=3,}\end{align}\) dan \(\begin{align}\mathrm{\int_{1}^{2}g(x)dx=4}\end{align}\)

Tentukan nilai dari:

\(\begin{align}\mathrm{\int_{0}^{2}f(x)dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{2}g(t)dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{2}^{0}5f(x)dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{2}^{0}[f(x)+g(x)]dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{2}^{1}[2f(t)+5g(t)]dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{0}^{1}3f(x)dx-\int_{2}^{1}4f(x)dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{2}^{0}g(x)dx+\int_{0}^{1}g(x)dx=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{1}^{3}f(t)dt-\int_{4}^{3}f(t)dt-\int_{2}^{4}f(t)dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{-1}^{0}g(t+1)dt-\int_{1}^{0}g(t+1)dt-\int_{-1}^{1}f(t+1)dt=\,...}\end{align}\)

\(\begin{align}\mathrm{\int_{2}^{3}f(t-2)dt-\int_{4}^{3}f(t-2)dt=\,...}\end{align}\)