Use a power series to approximate the definite integral, I, to six decimal places. 0.1 x arctan(5x) dx 0.

definite integral I = 0.001591  to six decimal places

Step-by-step explanation:

The definite integral is given as:

For arctanx , the power series is in the order

The next step is to substitute the value of 5x for x in the above equation;

So,

To  multiply both sides by (x); we have

Taking the integral on both sides with respect to x;

to six decimal places

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.