Use: F(x)=0.2((x - 3)^{2})(x + 1), bounded by the x axis, over [-1,2] Use the limit definition of Riemman Sum to find the earea shaded beneath the curve, round to 3 decimal places.

Isa Trevino 2021-01-05 Answered
Use:
F(x)=0.2((x  3)2)(x + 1), bounded by the x axis, over [-1,2]
Use the limit definition of Riemman Sum to find the earea shaded beneath the curve, round to 3 decimal places.
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Expert Answer

Brighton
Answered 2021-01-06 Author has 103 answers
Step 1
The length of the sub-intervals and the function is computed as follows,
Δ x=b  an
Δ x=3n
xi= 1 + 3in
Step 2
The formula for computing the area under the curve is,
12 0.2(x  3)2(x + 1)dx=limn  i=lnf(xi) Δ x
12(0.2x3  x2 + 0.6x + 1.8)dx=limn   i=lnf(1 + 3in)(3n)
Step 3
Thus, the area of the function, using the limit definition of Riemann sum is,
limn   i=lnf(1 + 3in)(3n)=limn   i=ln(0.2(1 + 3in)3  (1 + 3in)2 + 0.6(1 + 3in) + 1.8)(3n)
=limn   i=ln(9.6in + 5.4i3n3  14.4i2n2)(3n)
=limn   i=ln(28.8in2 + 16.2i3n4  43.2i2n3)
=0
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