Calculus Ii Exam Study Notes 2

Front 1

List three subtle substitution strategies.

Back 1

Multiply the fraction by a simplifying value

use properties of logs

re-writing fractions

Front 2

What subtle substitution strategy would you use to simplify the integral of:

(e^3z)/(e^2z-4e^-z)

Back 2

multiply the fraction by a simplifying value.

Front 3

What subtle substitution strategy would you use to simplify the integral of:

(sin^3(x))/(cos^5(x))

Back 3

re-writing fractions

Front 4

What subtle substitution strategy would you use to simplify the integral of:

(y^3)/(y^2+1)

Back 4

re-writing fractions (long division)

Front 5

How would you integrate the integral of:

cos^5(x)

Back 5

Split off a cosx and substitute cos^4(x) to (1-sin^2(x))^2. Then use u substitution.

Front 6

How would you integrate the integral of:

sin^4(x)

Back 6

Use half-angle formula to substitute sin^4(x) to

((1-cos2x)/2)^2. Foil then use the half angle formula again to substitute cos^2(2x) for (1+cos(4x))/2. Then integrate.

Front 7

how would you integrate the integral of

sin^m(x)cos^n(x) if m is odd.

Back 7

Split off a factor and use the pythagorean identities.

Front 8

how would you integrate the integral of sin^m(x)cos^n(x) if both m and n are even.

Back 8

use half-angle formulas to simplify.

Front 9

how would you integrate the integral of tan^m(x)sec^n(x) if n is even.

Back 9

Split off a sec^2(x) and let u=tanx

Front 10

how would you integrate the integral of tan^m(x)sec^n(x) if m is odd.

Back 10

split off secxtanx and let u=secx

Front 11

how would you integrate the integral of tan^m(x)sec^n(x) if m is even, and n is odd.

Back 11

write in terms of secx and use reduction formula.

Front 12

What would you let x equal to turn the following into multiplication?

a^2-x^2

Back 12

asinø

Front 13

What would you let x equal to turn the following into multiplication?

a^2+x^2

Back 13

atanø

Front 14

What would you let x equal to turn the following into multiplication?

x^2-a^2

Back 14

asecø

Front 15

How would you substitute

1/((x+4)(x-2))

Back 15

A/(x+4)+B/(x-2)

Front 16

How would you substitute

1/((x-2)^2)

Back 16

A/(x-2)+B/((x-2)^2)

Front 17

How would you substitute

1/((x^2+x+7x)(x-2))

Back 17

(Ax+B)/(x^2+x+7x)+C/(x-2)

Front 18

∫u(x)dv is

Back 18

uv-∫v(x)du

Front 19

L.I.P.E.T are the priorities for u.

Back 19

Logarithmic
Inverse trig functions
Polynomials
Exponentials
Trig Functions (basic)

Front 20

the definite integral U(x)V'(x) from a to b

Back 20

uv|(a,b)-∫(a,b)V(x)du