Review + FTC
What did Sarah tell us NOT forgot when answering indefinite integrals?
+ C !!
What should u be? integral of 2x(x^2+3)^2 dx
u = x^2+3
what acronym did Sarah tell us to learn for integration by parts?
LAPTE
what is the formula for average value?
1/(b-a) integral from a to b f(x)dx
what is cos^2(x) equal to?
1-sin^(x)
FTC: Given a function f(x) defined on an interval [a,b], then: the integral from a to b of f(x)dx is
F(B) - F(A)
integral from a = 1 to b = e of ((lnx)^2)/x
1/3
what should your u = and your dv= ? integral ((x^2)-4)cos(3x)dx
u = ((x^2)-4)
dv= cos(3x)
area below the curve: integral x(x^2+1)^5 a = 0 b = 1
21/4
integral cos(x)sqrt(sin(x))dx
(2/3)sin^(3/2)(x) +C
g(t) = the integral from 5 to t of 1/(1+x^4) what is g'(t)
1/(1+t^4)
compute the integral e^x(1+e^x)^10dx
((e^x+1)^11)/11 +C
compute the integral ln(x) dx
xln(x)-x+C
average value: f(x) = e^x on [0,2]
((e^2)-1)/2
what formula can help us solve the integral of sin^4(x)dx
double angle formula
Compute: the integral from of 9x^2+7x+sin(x)
3x^3+(7/2)x^2-cos(x)+C
compute the integral: e^(3x) dx
(1/3) e^(3x) +C
compute the integral (x+1)sin(x+1)dx
-(x+1)cos(x+1)+sin(x+1)+C
area b/w f(x) = x^3 and g(x) = x^2
1/12
integral sin^5(x)dx
-cos(x) +(2/3)cos^3(x) -1/5cos^5(x) +C
compute the integral (x^4 - 1)/x from a = 1 to b = 2
15/4 - ln(2)
compute the integral : (x/(x+2)^1/4)dx
(4/7)(x+2)^7/4 -(8/3)(x+2)^3/4 +C
compute the integral (x^3)(e^x)dx
(x^3)(e^x)-3(x^2)(e^x) +6x(e^x)-6(e^x)+C
area b/w curves: f(x)= x^3 -4x g(x) = 5x
81/2
integral sin^3(x)cos^5(x)dx
(1/8)cos^8(x)-(1/6)cos^6(x)+C