Question

Use the trapezoidal rule with n = 4 to approximate the integral with a upper bound of (1/3) and a Lower bound of 0 1/3 ∫ √ (1- 9x^2 )dx

******* by the way square root covers 1- 9x^2 in the integral fully for the entire equation

b. ) Use Simpson’s rule with n = 4 to approximate the same integral.

Answer #1

round your answer as needed

(a) Use the Trapezoidal rule with 4 equal partitions to
approximate
?
integral (from -1 to 1) (x^2 +1)dx
via the formula Tn =(∆x/2)(y0+2y1+...+2yn−1+yn )with n=4, and
∆x=(b−a)/n
(b) Compare the actual error, found by direct integration minus
the approximation, with the known error bound for the Trapezoidal
rule
|ETn| ≤ (f′′(c)/12n^2) (b−a)^3, 12n2
where c is a point at which the absolute value of the second
derivative is maximized.

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 4 0 ln(5 + ex) dx, n =
8
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule

Use the Trapezoidal Rule to approximate 4 on top ∫ on bottom 2
(9x^2+1) dx using n=4. Round your answer to the nearest tenth.
Evaluate the exact value of ∫42(9x2+1) dx and compare the results.
Trapezoidal Approximation ≈ Exact Value=

Use the trapezoidal rule with n=4 steps to estimate the
integral.
Integral from -1 to 1(x^2+6)dx
(-1 is on the bottom)

Use the Midpoint Rule with n = 4 to approximate the integral
from 1 to 3 of 1/x dx.

Using 4 equal-width intervals, show that the trapezoidal rule is
the average of the upper and lower sum estimates for the integral
from 0 to 8 of x squared, dx. typed solution only please

Use the trapezoidal rule with 4 rectangles to estimate the
integral of ex^2 dx from 1 to 3

Use the Trapezoidal Rule to approximate 8 on top ∫ on the bottom
5 ln(x^2+4) dx using n=3. Round your answer to the nearest
hundredth.

Use the Midpoint Rule with the given value of n to
approximate the integral. Round the answer to four decimal
places.
10
x2 + 5
dx, n = 4
2

2. Use Simpson’s rule with six
rectangles to estimate for using the Fundamental Theorem. ?Integral
from 0-4 x^3 dx

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