Evaluate the integral ∫2032x2+4dx. Your answer should be in the form kπ, where k is an integer. What is the value of k? (Hint: darctan(x)dx=1x2+1 ) k= 4 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)=32x2+4. Then, integrate it from 0 to 2, and call it S. S should be an infinite series ∑[infinity]n=0an . What are the first few terms of S?

Here is the correct computation of the question;

Evaluate the integral :

Your answer should be in the form kπ, where k is an integer. What is the value of k?

(Hint:  )

k = 4

(b) Now, lets evaluate the same integral using power series.

Then, integrate it from 0 to 2, and call it S. S should be an infinite series

What are the first few terms of S?

(a) The value of k = 4

(b)

Step-by-step explanation:

(a)

The value of k = 4

(b)

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w