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A student in Seoul estimates the area under y = x² from… | StemPy Lab
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A student in Seoul estimates the area under y = x² from x = 0 to x = 1 with 10 strips of equal width. She takes the height of each strip at its left end and adds the strip areas. What does she get?
Mathematics
Hard
High School (11–12)
Functions and Calculus › Application of Integrals
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A student in Seoul estimates the area under
y
=
x
2
y = x^2
y
=
x
2
from
x
=
0
x = 0
x
=
0
to
x
=
1
x = 1
x
=
1
with
10
10
10
strips of equal width. She takes the height of each strip at its left end and adds the strip areas. What does she get?
0.285
0.285
0.285
0.385
0.385
0.385
0.3325
0.3325
0.3325
1
3
\dfrac{1}{3}
3
1
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← The figure shows the profile of a trench dug across a road. It follows the curve y = x² - 1 for -2 ≤ x ≤ 2, with x and y in metres. The road crew wants the total area between the profile and the line y = 0, counting the parts above and below the line as positive. What is this total area, in square metres?
A cycle path in a nature reserve has the profile y = (x - 1)(x - 2)(x - 3) for 1 ≤ x ≤ 3, with x in kilometres and y in kilometres, as in the figure. The path crosses a reference line y = 0 at three points. The reserve wants the total area between the profile and the reference line. What is this area, in square kilometres? →
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Functions and Calculus › Application of Integrals
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