MATH 232 Midterm 1

tan²x +1

tan²x +1

= sec²x

cot²+1

= csc²x

sin²x+cos²x

= 1

2sinxcosx

= sin(2x)

2cos²x-1

= cos(2x)

1/2(1-cos(2x))

= sin²x

1/2(1+cos(2x))

= cos²

sec²x-1

= tan²x

(1-cos(6x))/2

= sin²(3x)

sinx

**If COS is ODD, make u=

cosx

**If SIN is ODD, make u=

secx, secxtanx

**If TAN is ODD, make u= & pull off a…

tanx, sec²x

**If SEC is EVEN, make u= & pull off a…

tan²x= sec²-1, integration by parts

**If TAN is EVEN, and SEC is ODD, use ____ and then do ____ with remaining sec

u= sqrt(a) * sinx

Trig sub: a-x²

u= sqrt(a) * tanx

Trig sub: a+x²

u= sqrt(a) * secx

Trig sub: x²- a

(secxtanx + ln |secx+tanx|)/2 + C

Integral of sec³x dx

secx + C

Integral of secxtanx dx

tanx + C

Integral of sec²x dx

ln |secx + tanx| + C

Integral of secx dx

-ln |cosx| + C

Integral of tanx dx

uv - integral of v * du

Integration by parts

1/3(pi)(height)²(3R-height)

Volume of spherical cap

Integral from a to b: pi(f(x))² dx

Volume of Revolutions: Disks

Integral from a to b: pi(f(x)²-g(x)²) dx

Volume of Revolutions: Washer