Further Calculus

Question 1

Answer 1

Question 2

Answer 2

It was 3 instead of root 3 but idk how

Question 3

Answer 3

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

What the formula for the mean function?

Answer 7

Question 8

Answer 8

Chat GTP calls the cos thing the product to sum rule

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

The integral of 0 is C

Question 12

Answer 12

Question 13

Answer 13

Two methods.
Method 1: using substitution and getting it as 1- u ^2
Method 2: using standard results and getting the coefficient of x^2 = -1

Question 14

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Simple smaller substitutions to save time, making use of formula sheet

Answer 19

Using first principles wastes too much time