Adding eq. (i) and (ii),
$21=\int\limits_{0}^{\frac{\pi}{2}}\bigg[\frac{\sin^{\frac{3}{2}}\text{x}}{\sin^{\frac{3}{2}}\text{x}+\cos^{\frac{3}{2}}\text{x}}+\frac{\cos^{\frac{3}{2}}\text{x}}{\cos^{\frac{3}{2}}\text{x}+\sin^{\frac{3}{2}}\text{x}}\bigg]\text{dx}=\int\limits_{0}^{\frac{\pi}{2}}\bigg[\frac{\sin^{\frac{3}{2}}+\cos^{\frac{3}{2}}\text{x}}{\sin^{\frac{3}{2}}\text{x}+\cos^{\frac{3}{2}}\text{x}}\bigg]\text{dx}$
$\Rightarrow\ \ 21=\int\limits_{0}^{\frac{\pi}{2}}1\ \text{dx}=\bigg(\text{x}^{\frac{\pi}{2}}_{0}\bigg)\ \Rightarrow\ \ 21=\frac{\pi}{2}\ \Rightarrow\text{I}=\frac{\pi}{4}$
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| Values of X: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P(X) | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
Determine:
$\text{P}(\text{X}<3),\text{P}(\text{X}\geq3),\text{P}(0<\text{X}<5).$f(x) = x + 1, g(x) = ex