7. Antiderivatives & Indefinite Integrals

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

Checking Antiderivative Formulas

Right, or wrong? Say which for each formula and give a brief reason for each answer.

∫tanθ sec²θ dθ = (1/2) sec²θ + C

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.

πcos πx

If F(x) = x² - 3x + C and F (-1) = 4 , what is the value of C?

Checking Antiderivative Formulas

Verify the formulas in Exercises 57–62 by differentiation.

∫csc²((x − 1)/3)dx = −3cot((x − 1)/3) + C

Finding antiderivatives. Find all the antiderivatives of the following functions. Check your work by taking derivatives.

g(s) = 1 / (s² + 1)

Find the antiderivative of the following function.

$f\(\left\)(x\(\right\))=10x^9$

Finding Antiderivatives

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

−πsin 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.

−π csc (πx/2) cot (πx/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.

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.

2x

Find all functions whose derivative is f'(x) = x + 1.

Finding Antiderivatives

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

4 sec 3x tan 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.

sec²x