Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

# Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.?

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• david
Lv 7
8 months ago

a. Trap ... (b - a)/n = width of each subinterval

(3-2)/10 = 0.1

sub intervals -- (2, 2.1), (2.1,2.2), (2.2,2.3) etc

area of each trap. = (1/2)[f(left end pt) + f(right end pt)](width)

1st sub = (1/2)[f(2.0) + f(2.1)](0.1)

2nd sub = (1/2)[f(2.1) + f(2.2)](0.1)

3rd sub = (1/2)[f(2.2) + f(2.3)](0.1)

..... etc

10th sub = (1/2)[f(2.9) + f(3.0)](0.1)

===========================================

answer is the sum of all sub intervals

you can do the rest, just substitute into the function and do the math ...

good luck.

==========================================

Midpoint rule === same subintervals as above

midpoint of 1st sub = (2.0 + 2.1)/2

midpoint of 2nd sub = (2.1 + 2.2)/2

midpoint of 3rd sub = (2.2 + 2.3)/2

..... etc ...

Area of 1st sub = f(mid pt 1)*(width)

Area of 2nd sub = f(mid pt 2)*(width)

.... etc ...

Answer is sum of all sub areas above

... again just substitute and start calculating

... Good luck -- and get started it will take some time.