t) Find the area under y = -x² + 1x + 12 and above the x-axis using Riemann sums. ·b S² (-2²² + a and b = (a) This area is equal to where a = −x² + 1x + 12) dx
t) Find the area under y = -x² + 1x + 12 and above the x-axis using Riemann sums. ·b S² (-2²² + a and b = (a) This area is equal to where a = −x² + 1x + 12) dx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:t) Find the area under y = -x² + 1x + 12 and
above the x-axis using Riemann sums.
(a) This area is equal to
where a =
(b) The Riemann sum for this integral is
ΣR=11+
Sn
·b
• (-x² + 1x +12) dx
a
and b =
=
Σk=1k+
(c) As a function of n
Sn
=
(d) The area is then A
=
Σ_1 k2.
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