7. Antiderivatives & Indefinite Integrals

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.

-(1/2)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.

(-3/2)csc²x(3x/2)

For the following function $f\(\left\)(x\(\right\))$, find the antiderivative $F\(\left\)(x\(\right\))$ that satisfies the given condition.

$f\(\left\)(x\(\right\))=100x^{99}$; $F\(\left\)(1\(\right\))=101$

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.

2 - 5 / x²

Checking Antiderivative Formulas

Right, or wrong? Give a brief reason why.

∫−15(x + 3)² / (x − 2)⁴ dx = ((x + 3)/(x − 2))³ + 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.

x⁷

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

ƒ(y) = - 2/y³

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⁻³/2 + x²