Estimate the area under the curve f ( x ) = x 2 over the interval [0,10] with 5 strips using Left Riemann Sums?

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Estimate the area under the curve             f              (        x        )              =          x      2       over the interval [0,10] with 5 strips using  Left Riemann Sums?

Bronchialyo2 · Accepted Answer

The left riemann sum requires you to evaluate the functional value at a certain x value, as shown below, using the lower number in each interval stated above as your x term:      1    .    A    r    e          a      1        =          f              (        0        )              ⋅    2    =          0      2        ⋅    2    =    0        2    .    A    r    e          a      2        =          f              (        2        )              ⋅    2    =          2      2        ⋅    2    =    8        3    .    A    r    e          a      3        =          f              (        4        )              ⋅    2    =          4      2        ⋅    2    =    32        4    .    A    r    e          a      4        =          f              (        6        )              ⋅    2    =          6      2        ⋅    2    =    72        5    .    A    r    e          a      5        =          f              (        8        )              ⋅    2    =          8      2        ⋅    2    =    128        T    o    t    a    l    A    r    e    a    =    0    +    8    +    32    +    72    +    128    =    240  Left riemann sum would be 240 for the graph       y    =          x      2       on the interval [0,10]

dhopeefreshnwn · Accepted Answer

f              (        x        )              =          x      2            Δ    x    =                  10        -        0            5        =    2        L    R    S    =                  ∑                  r          =          0                4                    f              (                  x          i                )                   Δ          x      i                                           =    240        A    r    e    a    =                  ∫        0        10                         x      2                   d      x                                           =          1      3                                [                      x            3                    ]                0        10                                                 =          1000      3                                           =    333.3333    ...

Estimate the area under the curve f(x) = x^2 over the interval [0,10] with 5 strips using Left Riemann Sums?

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