U6: Integration formulas for Basic and Trigonometric Functions, Properties of indefinite integrals, fundamental theories of calculus, net chance, average value, future value. and postition/velocity formulas

∫c • f(x)dx= c • ∫f(x)dx

∫[f(x) ± g(x)]dx = ∫f(x)dx ± ∫g(x)dx

∫x^n dx = x^(n+1)/(n+1) +C

sinx +C

tanx +C

secx +C

-cosx+ C

-cotx+ C

-cscx +C

e^x +C

ln|x| +C

If f is continuous on [a,b], then

∫[b,a] f(x)dx= F(b)-F(a)

where F is the antiderivative of f.

Basically, you find the antiderivative [F(x)], and then define the function with the b and a values given [F(b) - F(a)].

d/dx {∫[x,a] f(t)dt = f(x)}

ex: d/dx {∫[x,3] t ln(t-5)dt = x ln (x-5)

If R represents the rate at which a quantity W is changing W(t) is antiderivative of R(t), then:

∫[b,a] R(t)dt = W(b) - W(a)

If R represents the rate at which a quantity W is changing W(t) is antiderivative of R(t), then:

1/(b-a)∫[b,a] R(t)dt

If R represents the rate at which a quantity W is changing W(t) is antiderivative of R(t), then:

[W(b)- W(a)]/(b-a)

If R represents the rate at which a quantity W is changing W(t) is antiderivative of R(t), then:

W(b) = W(a) + ∫[b,a] R(t)dt

-ln|cosx| + C

ln|secx+tanx| +C

ln|sinx| + C

-ln|cscx+cotx| + C