The definite integral is .

(a)

Determine by Trapezoidal Rule:

Here ,  and .

Where, and .

End points are and .

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(b)

Determine by Midpoint Rule:

Number of subintervals are .

Here ,  and .

Width of the interval is .

, where .

Mid points are and .

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Graph:

Graph the function :

Trapezoidal Rule:

Midpoint Rule:

Observe the graphs:

Trapezoidal estimation is underestimate and midpoint estimation is overrestimate.

Thus, True value lies in between the above estimations.

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