Work through the following steps to evaluate (² + 4x + 7)dx. a) We know that a = and b = b) Using n subintervals, Ax= c) Assume that the sample points in each interval are right endpoints. Find the following sample points: #1 I2 x3 = In general, the ith sample point is #₁ = Note: your answer will be an expression in terms of i || 000

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Work through the following steps to evaluate
T
(x² + 4x + 7)dx.
a) We know that a =
and b=
b) Using n subintervals, Ax =
c) Assume that the sample points in each interval are right endpoints. Find the following sample points:
I1 =
I2 =
x3 =
In general, the ith sample point is x₁ =
Note: your answer will be an expression in terms of i
and n.
d) Now find the sum of the areas of n approximating rectangles. Note: your answer will be an expression in
terms of n.
n
Σf(x) Ax=
=
i=1
e) Finally, find the exact value of the integral by letting the number of rectangles approach infinity.
n
[₁² (2²+
(x² + 4x + 7) dx = lim f(x₁) Ax=
848
i=1
000
Transcribed Image Text:Work through the following steps to evaluate T (x² + 4x + 7)dx. a) We know that a = and b= b) Using n subintervals, Ax = c) Assume that the sample points in each interval are right endpoints. Find the following sample points: I1 = I2 = x3 = In general, the ith sample point is x₁ = Note: your answer will be an expression in terms of i and n. d) Now find the sum of the areas of n approximating rectangles. Note: your answer will be an expression in terms of n. n Σf(x) Ax= = i=1 e) Finally, find the exact value of the integral by letting the number of rectangles approach infinity. n [₁² (2²+ (x² + 4x + 7) dx = lim f(x₁) Ax= 848 i=1 000
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