Exam 1

Question 1

For trig expressions, when denominator is 3 or 6, use the numbers for the triangle

Answer 1

1, 2(hyp), sqrt 3 (opp)

Question 2

For trig expressions whose denominator is 2 or 4

Answer 2

Use the numbers 1, 1, sqrt 2 (hypt)

Question 3

Chain rule

Answer 3

Multiply function by exponent then subtract the exponent by 1, then multiply the expression by the derivative of the inside

Question 4

Pythagorean, identities of sine and cosine

Answer 4

Sine squared X plus cosine squared X equals one

Question 5

Integration by parts

Answer 5

You times V minus the integral of V times DU

Question 6

For trigonometric substitution, if you have radical a squared minus X squared

Answer 6

let x=asin0 and dx=acos0d0

Question 7

For integrals with trigonometric substitution, the steps are

Answer 7

Write what x and dx equals
Substitute the x’s and dx
Simplify the radical by factoring and seeing if you get any identities and take the sqrt
See if anything cancels

Question 8

For trigonometric substitution, if you have radical a squared plus x squared

Answer 8

Let x=atan0 and dx=asec^20d0

Question 9

For trigonometric substitution, if you have radical x^2 minus a^2

Answer 9

Let x=asec0 and dx=asec0tan0d0