The following table shows corresponding values of xxx and yyy for a curve with equation y=g(x)y = g(x)y=g(x). The values of yyy are rounded to 3 decimal places.
| xxx | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| yyy | 1.141 | 3.562 | 6.890 | 4.121 | 0.985 |
Using the trapezium rule with all the values of yyy in the given table, obtain an estimate for
∫04g(x) dx \int_{0}^{4} g(x) \, dx ∫04g(x)dxgiving your answer to 2 decimal places.
Use your answer to part (a) to estimate (i)
∫04(g(x)+3) dx \int_{0}^{4} (g(x) + 3) \, dx ∫04(g(x)+3)dx(ii)
∫26g(x−2) dx \int_{2}^{6} g(x-2) \, dx ∫26g(x−2)dx
