Help With Antiderivatives

[Allen]

Well I somewhat understand antiderivatives, but I am still stuck on my last three math problems. If you could possibly help it would be appreciated. Thanks.

1. Find antiderivatives for the following functions:

(a) f(x) = x^2- e^3x

(b) v(t) =3/t- e^-t

© x(s) = a * cos (s/b)

*They are also in attachment, thanks*

[∫ Jorge δx]

Have you had a look at your data booklet? All the standard integrals should be there.

If you haven't, either way, remember a few basic things:

When you do anti-differentiation (better known as integration) with polynomials all you do is you add 1 to the exponent and then divide by the new exponent, in other words, the anti-derivative of xⁿ is xⁿ⁺¹/n+1.

Remember also that e^x is its own rate of change, so the integral of e^x is e^x. Since you have e^ax, the integral will be e^ax/a. Same concept really.

When you have more than one term, you can separate them and integrate each term separately. So let's say we have (integral (x+1)), it's exactly the same as (integral)x + (integral)1.

When you have a function in the denominator of a fraction, and its numerator is a multiple of its derivative, then you know that the integral is the natural logarithm of that function. In your data booklet, there should be something along the lines of "when f(x)=lnx and f'(x)=1/x", just apply this concept.... Backwards .

Last but not least, remember that sine and cosine functions are derivatives (and hence, integrals) of each other (playing around with some negative signs here and there).

Hope to have helped.

[Allen]

You did I just am still having trouble with c, the numbers/ variables inside the parentheses are confusing me. Thanks for you help.

[∫ Jorge δx]

You're integrating with respect to s for c.

So your integral would be something like -absin(s/b).

When you work with trigonometric functions during integration, you divide by the derivative of the function inside the trigonometric function.