7. Antiderivatives & Indefinite Integrals

Suppose $F\left(x\right)$ is an antiderivative of $f\left(x\right)$. Which of the following statements about the indefinite integral $\int f\left(x\right) dx$ is true?

Let $h\left(x\right)$ be an antiderivative of the function $f\left(x\right)=x^3+\frac{-\sin x}{x^2}+2$. Which of the following is a correct expression for $h\left(x\right)$?

Suppose the graph of a function $f$ is shown below. Which of the following graphs could represent an antiderivative $F$ of $f$?

Find the antiderivative of the following function.

$f\(\left\)(x\(\right\))=5x^4$

Find the antiderivative of the following function.

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

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

$f\(\left\)(x\(\right\))=5x^4$; $F\(\left\)(0\(\right\))=1$

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$

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

Describe the set of antiderivatives of ƒ(x) = 1

Give the antiderivatives of xᵖ . For what values of p does your answer apply?

Give the antiderivatives of 1/x.

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

ƒ(x) = 2 sinx + 1

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

p(x) = 3 sec² x

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

ƒ(y) = - 2/y³

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

ƒ(x) = eˣ