Unit 6 Flashcards
Area of a trapezoid?
(y1+y2) * Δx/2
Antiderivative of sin(x)
-cos(x)+C
Antiderivative of cos(x)
sin(x)+C
Antiderivative of sec^2 (x)
tan(x)+C
Antiderivative of sec(x)tan(x)
sec(x)+C
Antiderivative of csc(x)cot(x)
-csc(x)+C
Antiderivative of csc^2 (x)
-cot(x)+C
Antiderivative of 1 / (1+x^2)
arctan(x)+C
Antiderivative of 1 / (abs(x)*(sqrt(x^2 - 1))
arcsec(x)+C
Antiderivative of a^x
( (a^x) / ln(a) ) + C
Antiderivative of e^x
e^x + C
Antiderivative of 1/x
ln(abs(x)) + C
Antiderivative of 0
C
integral of du / (a^2 + u^2)
(1/a) * arctan(u/a) + C
integral of du / sqrt(a^2 - u^2)
arcsin(u/a) + C
integral of du / abs(u)*sqrt(u^2 - a^2)
(1/a) arcsec(u/a) + C
integral of du/u
ln(abs(u)) + C
What should you remember about MRAM, LRAM, and RRAM, with equal length subintervals?
You can factor out Δx
When approximating with LRAM, RRAM, MRAM, and the trapezoid rule, remember to…
use a wavy equals sign to signify when something is approximated
Riemann sum notation?
See notes. (makes more sense than as a flashcard).
Steps you sometimes forget?
Breaking apart fractions into sums when possible.
Including constants in with u.
+C on the end of indefinite integral.
Basic arithmetic, forgetting steps, numbers, and signs.
Adding dx to the end of an integral.
1/x^n = x^(-n)
Mistakes you sometimes make?
Breaking apart the denominator.
Not fully resolving ‘x’ when using u substitution.
-1/2 + 1 = 1/2 not -3/2
Improperly
Mistakes you sometimes make?
Breaking apart the denominator.
Not fully resolving ‘x’ when using u substitution.
-1/2 + 1 = 1/2 not -3/2
In a Riemann sum, what is delta x?
(b-a)/n
