7. Antiderivatives & Indefinite Integrals

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)] 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)

Finding Antiderivatives

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

(2/3)x⁻¹ᐟ³

Finding Antiderivatives

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

-(1/3)x⁻⁴ᐟ³

Finding Antiderivatives

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

-(1/2)x⁻³ᐟ²

Finding Antiderivatives

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

sin πx − 3sin 3x

Finding Antiderivatives

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

πcos πx

Finding Antiderivatives

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

sec²x

Finding Antiderivatives

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

-sec²(3x/2)

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)csc²x(3x/2)

Finding Antiderivatives

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

csc x cot 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.

−π csc (πx/2) cot (πx/2)