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elena55 [62]
2 years ago
11

Pleeeeeaseee help meeeee computing definite integral by appealing to geometric formulas

Mathematics
1 answer:
Lana71 [14]2 years ago
4 0

Plotting the functions is highly recommended.

For A, the area under f(x)=3 over the interval [1, 2] is the area of rectangle with height 3 and width 2 - 1 = 1, so the area is

\displaystyle\int_1^23\,\mathrm dx=3\cdot1=3

For B, the area under f(x)=1-|x-1| plotted over the interval [0, 2] is the area of a triangle with height 1 and base length 2, so the area is

\displaystyle\int_0^2(1-|x-1|)\,\mathrm dx=\frac12\cdot1\cdot2=1

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