Applications


Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).


Find:


∫f(x) dx

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

1 / x²

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

2 - 5 / x²

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

1 / 2x³

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

(3/2)√x

Applications

Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).

Find:

∫[−f(x)] dx

Applications

Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).

Find:

∫[f(x) + g(x)] dx

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

√x + 1/√x

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

1/(3³√x)