Jamie took an 8-week keyboarding class. at the end of each week, she took a test to find the number of words she could type per minute and found out she improved the same amount each week. before jamie started the class, she could type 25 words per minute, and by the end of week 8, she could type 65 words per minute.

When Jamie started the class, she could type 25 words per minute.
After she finished the class, she was able to type 65 words per second.

Based on this, the extra number of words the Jamie learnt to type during the complete duration of the class (her improvement throughout the whole class) can be calculated as follows:
improvement = 65 - 25 = 40 words/minute

Since the improvement of Jamie was equally distributed throughout each week of the eight week, therefore, each week she learnt to type 40/8 = 5 words per minute more than the previous week.

To make it simpler:
Before starting the class, Jamie could type 25 words/minute
After week 1, Jamie could type 25 + 5 = 30 words/minute
After week 2, Jamie could type 30 + 5 = 35 words/minute
After week 3, Jamie could type 35 + 5 = 40 words/minute
After week 4, Jamie could type 40 + 5 = 45 words/minute
After week 5, Jamie could type 45 + 5 = 50 words/minute
After week 6, Jamie could type 50 + 5 = 55 words/minute
After week 7, Jamie could type 55 + 5 = 60 words/minute
After week 8, Jamie could type 60 + 5 = 65 words/minute

To solve this integral, what you can do is split it up as follows: (1) ∫40(x2−4)dx=∫40(x2)dx−∫40(4)dx. to integrate  4  as an  indefinite integral, a good rule of thumb is  by  an equation below  for  polynomials; . (2) ∫xa=xa+1a+1+c , where a is any number. c denotes some constant that is crucial when doing