Test 1 Review (Calc II)Questions and and answers

Test 1 Review (Calc II)

✅✅-Half angle identities
(Trig substitution)
If all values are even, what do we use? -

√(a²-x²) - ✅✅-x=asinθ
√(a²+x²) - ✅✅-x=atanθ

√(x²-a²) - ✅✅-x=asecθ

∫√u - ✅✅-(2/3)u^3/2

∫sec(x)dx= - ✅✅-ln(|sec(x)+tan(x)|)+C

Anti-derivative of (3/4)sin(4x)? - ✅✅--(3/16)cos(4x)

Anti-derivative of e^3x - ✅✅-(1/3)e^3x

antiderivative of 1/1+x² - ✅✅-tan⁻¹(x)

antiderivative of tan(x) - ✅✅-ln(|sec(x)|)

average value of a function on an interval [a,b] - ✅✅-(1/b-a) ∫f(x)dx

Derivative of 2/x - ✅✅--2/x²

Derivative of arctan(x) - ✅✅-1/1+x²

Derivative of e^3x - ✅✅-3e^3x

Derivative of ln(6x+1) - ✅✅-6/6x+1

Derivative of ln(9x+1) - ✅✅-9/9x+1

Derivative of sec(x) - ✅✅-sec(x)tan(x)

Derivative of sec²(x) - ✅✅-tan(x)

derivative of tan²(x) - ✅✅-2sec²(x)tan(x)


✅✅
Double-Angle Identity
cos(2x)= - -cos²(x)-sin²(x)