Calc question help!?

Question

How large should n be to guarantee that the Simpson's Rule approximation to 17e^x^2 from 0-1 is accurate within .00001?

Answer 1

Step 1:

The function is .

Consider the function as

Find the fourth derivative of .

Differentiate with respect to .

Differentiate with respect to .

Differentiate with respect to .

Again differentiate with respect to .

It is obvious that is increasing and it has the absolute maximum in the interval at .

Step 2:

Consider the number

Find the number using Simpsons error formula.

Simpsons error formula is .

Substitute , in above formula.

Here error less than .

Determine within the error less than .

Solution:

Approximate value of is 38.