Exam 2

Question 1

Arc length

Answer 1

∫ᵇₐ √[ 1 + (f’(x))² ] dx

Question 2

Integration by parts

Answer 2

∫u dv = uv - ∫v du

Question 3

Derivative of ln(10x)

Answer 3

1/x
because ln(10x) = ln(10) + ln(x)
ln(10) is a constant so its derivative is zero

Question 4

Useful trig identities

Answer 4

sin²(x) = 1/2 - 1/2 cos(2x)
sec²(x) = 1 + tan²(x)

Question 5

When 1 round of integration by parts results in original equation in integral

Answer 5

Given i is the original integral to be solved

i = stuff - #i
i = stuff/(1+#)

Question 6

Notes for reduction formula

Answer 6

If 2 different trig function use an identity to make the functions the same

Then operate on 2 integrals

or

Use reduction formula a repeated number if times if power is higher than 3