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value of z= 96

of 7 a C 88 > Task 3: Answer the following: a. Evaluate: 57% z cos(x) sin?(x) dx (10 Marks) 2 b. The moment of inertia, I, of

Task 3: Answer the following:

a. Evaluate: \(\int_{\frac{\pi}{2}}^{\pi} \boldsymbol{Z} \cos ^{3}(x) \sin ^{2}(x) d x\)

b. The moment of inertia, \(I\), of \(a\) rod of mass ' \(m^{\prime}\) and length \(4 r\) is given by \(I=\int_{0}^{4 r}\left(\frac{Z m x^{2}}{2 r}\right) d x\) where \(^{\prime} x^{\prime}\) is the distance from an axis of rotation. Find \(I \)

Task 4: Answer the following:

Using the Trapezoidal rule, find the approximate the area bounded by the curve

\(y=\boldsymbol{Z} e^{\left(\frac{x}{2}\right)}\), the \(\mathrm{x}\) -axis and coordinates \(x=0, x=6 .\) Consider \(n=20 .\) Also, find the

accurate area of the above curve using integration and compare the areas found by

Trapezoidal and analytical integration methods. \(\quad\)

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