I just can't seem to get a handle on them. Derivatives are a piece of cake, but integrals always seem to stump me. For example, I can't even integrate cos^3(x)sin(x)dx.
2007-01-15 02:09:20 · 2 answers · asked by Ændru 5 in Science & Mathematics ➔ Mathematics
When computing integrals, always look to see if you can find a function together with its derivative in the integrand. If you can, there is a good chance it can be computed by change of variables (the so-called u-substitution).
In this case there is a cos x and a sin x in the integrand, and you know that the derivative of cos x is -sin x, so it seems the substitution u = cos x will work here. Then du = -sin x dx, and the integral you now have is
Integral(-u^3 du),
which of course you already know how to do. The antiderivative is -(1/4)u^4, which is, (-1/4)(cos x)^4.
2007-01-15 02:24:25 · answer #1 · answered by acafrao341 5 · 1⤊ 0⤋
u-substitution
like acafraco said
:-(
2007-01-15 10:26:09 · answer #2 · answered by a_math_guy 5 · 1⤊ 0⤋