Checking Antiderivative Formulas


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


∫√(2x + 1) dx = √(x² + x +C)

Initial Value Problems

Solve the initial value problems in Exercises 89–92.

dy/dx = (𝓍 + 1/𝓍)² , y(1)= 1

Finding Indefinite Integrals

Find the indefinite integrals (most general antiderivatives) in Exercises 73–88. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫ sec² s/10 ds

Applications

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

Find:

∫f(x) dx

Finding Indefinite Integrals

Find the indefinite integrals (most general antiderivatives) in Exercises 73–88. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫ 1/( r + 5)²dr

Identifying Extrema

In Exercises 41–52:

a. Identify the function’s local extreme values in the given domain, and say where they occur.

f(t) = 12t − t³, −3 ≤ t < ∞

Identifying Extrema

In Exercises 63 and 64, the graph of f' is given. Assume that f has domain (-2, 2).

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a. Either use the graph to determine which intervals f is increasing on and which intervals f is decreasing on, or explain why this information cannot be determined from the graph.