Use a taylor series to approximate the following definite integrals. retain as many terms as needed to ensure the error is less than 10−4. ∫0.201+x4√dx

I= 0.40102036

Step-by-step explanation:

∧ = raise to power

Given the equation

F(x) = √x² + 1.0

Now recalling the Taylor Series in respect to the approximation  for degree n at x = a

Therefore, it is given by :

f(x) = f(a) + f° (a) ((x - a)) + ( 1/2) f°° (a)((x -a)² + (1/n!) f∧n (a) ((x - a) ∧ n

Referring back to the Taylor Series

f(x) = - x ∧8/8 + x ∧ 4/2 + 1

If we integrate the Taylor series, we get,

f°(x) = - x ³*³/72 + x∧5/10 + x

At this point, we apply limit (lim) to the integrals

I = ∫ lim(0.4) (0) f(x) dx

I = ∫ (- x ∧8/8 + x ∧ 4/2 +1)dx

I = [ ( -x³*³/72 + x∧5/10 +x)]lim(0.4) lim(0)

The final answer then is:

I= 0.40102036

answer: the four apples you took away.

step-by-step explanation:

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.