Math, asked by yadavanuja01, 1 month ago

Question 6:
Evaluate S (1+r3
S*(1+) dx by using the
Trapezoidal rule divide the interval
[0,2] into 4 equal sub-intervals
5.29
6.25
6.76
5.76​

Answers

Answered by soniathakran168
0

Answer:

> 5. Numerical Integration

Review of Interpolation

Find pn(x) with pn(xj ) = yj , j = 0, 1, 2, . . . , n. Solution:

pn(x) = y0`0(x) + y1`1(x) + . . . + yn`n(x), `k(x) = Qn

j=1,j6=k

x−xj

xk−xj

.

Theorem

Let yj = f(xj ), f(x) smooth and pn interpolates f(x) at

x0 < x1 < . . . < xn. For any x ∈ (x0, xn) there is a ξ such that

f(x) − pn(x) = f

(n+1)(ξ)

(n + 1)! (x − x0)(x − x1). . .(x − xn)

| {z }

ψ(x)

Example: n = 1, linear:

f(x) − p1(x) = f

00(ξ)

2

(x − x0)(x − x1),

p1(x) = y1 − y0

x1 − x0

(x − x0) + y0.

5. Numerical Integration

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