Question to test your Riemann Sums knowledge

Question

A pot of soup is placed on a stove at time $t equals 0$ . Its temperature, $T$ , in degrees Celsius for $0 is less than or equal to t is less than or equal to 100$ , is measured at the following times (in seconds).

The function is assumed to be continuous and strictly increasing on the given interval. Approximate $\frac{1}{100} \int_{0}^{100} T (t) d t$ using the Trapezoid Rule for nonuniform grids. What does this value represent in the context of the problem?

Accepted Answer

1100∫0100T(t) dt≈60.4\frac{1}{100}\$$int_0$$^{100}T(t)\,dt\approx60.4This value means that the average temperature of the soup over the first 100100 seconds is about 60.4 ∘C60.4~^{\circ}	ext{C}

Answer

1100∫0100T(t) dt≈63.8\frac{1}{100}\$$int_0$$^{100}T(t)\,dt\approx63.8This value means that the average temperature of the soup over the first 100100 seconds is about 63.8 ∘C63.8~^{\circ}	ext{C}

Answer

1100∫0100T(t) dt≈60.4\frac{1}{100}\$$int_0$$^{100}T(t)\,dt\approx60.4This value means that the exact temperature of the soup after 5050 seconds is 60.4 ∘C60.4~^{\circ}	ext{C}

Answer

1100∫0100T(t) dt≈63.8\frac{1}{100}\$$int_0$$^{100}T(t)\,dt\approx63.8This value means that the exact temperature of the soup after 5050 seconds is 63.8 ∘C63.8~^{\circ}	ext{C}

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