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BC Calc - Unit 6

QuestionAnswer
∫u'e^u e^u + C
∫f'(g(x)) ⋅ g'(x) f(g(x)) +C
∫1/√1-x^2 arcsinx + C
∫-1/√1-x^2 arccosx + C {or} -arcsinx + C
∫1/1+x^2 arctanx + C
∫-1/1+x^2 arccotx + C {or} -arctanx + C
∫1/|x|√x^2-1 arcsecx + C
∫-1/|x|√x^2-1 arccscx + C {or} arcsecx + C
A Right Riemann Sum In An Over-Approximation When... the graph is increasing
A Left Riemann Sum In An Over-Approximation When... the graph is decreasing
A Right Riemann Sum In An Under-Approximation When... the graph is decreasing
A Left Riemann Sum In An Under-Approximation When... the graph is increasing
Steps To Find f'(x) When f(x)=∫tdt derivative and integral cancel, plug in top limit for t, solve
Integration By Parts Theorem ∫udv = uv - ∫vdu
Sigma Notation ∑ = sigma notation // n=upper bound // i=index // # i equals=lower bound
EVT every continuous function on [a,b] has both an absolute maximum and minimum
In Word Problems, f(x) Is... a number
In Word Problems, f'(x) Is... a rate
In Word Problems, f''(x) Is.. a rate of a rate
Absolute Minimums & Maximums Can Occur At... endpoints & critical values
∫x^-1dx Is Equal To... ∫1/xdx {or} ln|x|
When Writing The Solution To An Indefinite Integral, Always Add... + C
∫a^xdx (1/lna)(a^x) + C
∫f(u)u'dx f(u) + C
∫(a^u)(u')dx (1/lna)(a^u) + C
∫du/√a^2 - u^2 arcsin(u/a) + C
∫du/a^2 + u^2 (1/a) ⋅ arctan(u/a) + C
∫du/u√u^2-a^2 (1/a) ⋅ arcsec(|u|/a) + C
Steps To Integrate With Long Division divide numerator by denominator, plug answer back into intergal, solve integral
Completing The Square x^2+bx+c = x^2 + bx + (b/2)^2 - (b/2)^2 + C = (x+b/2)^2 - (b/2)^2 + C
When Picking The U In An Integration By Parts, You Should Use... L.I.A.T.E.
L.I.A.T.E. Stands For... logarithm, inverse trig, algebraic, trigonometric, exponential
Tabular Method first column: alternating signs starting with + // second column: derive u-value until 0 // third column: intergrate dv-value
Linear Factors (a*x + b*) / (a**x + b**) (a***x + b***) = [A / (a**x + b**)] + [B / (a***x + b***)
Created by: abievans
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