**Problem : **
Consider the function *f* (*x*) = *x*^{2} + 1 on the interval [0, 2].
Using four subdivisions, find the left-hand approximation, *L*_{4}, of the
area under the curve of *f* on the interval indicated.

Δx | = = = | ||

L_{4} | = f (0) + f () + f (1) + f () | ||

= 1 + +2 + | |||

= = |

**Problem : **
For the same function, using four subdivisions, find the right-hand sum, *R*_{4}.

R_{4} | = f () + f (1) + f () + f (2) | ||

= +2 + + 5 | |||

= = |

**Problem : **
For the same function, using four subdivisions, find the midpoint sum, *M*_{4}.

M_{4} | = f () + f () + f () + f () | ||

= + + + | |||

= = |

Notice that on the interval in question,

**Problem : **
Find

f (x_{k})Δx for f (x) = 2x on [0, 2] |

To solve this problem, notice that the graph of

(2)(4) = 4 |

**Problem : **
Find

f (x_{k})Δx for f (x) = on [0, 3] |

To solve this problem, notice that the graph of

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