← MATH 01130 · Calculus I
MATH 01130 · Integrals (intro)
Antiderivatives
Definition
An antiderivative of f is a function F with F′=f. Indefinite integral ∫f(x) dx = F(x)+C. Families differ by a constant.
Read this
Reverse the derivative rules: power rule becomes ∫xⁿ dx = xⁿ⁺¹/(n+1)+C (n≠−1).
Check by differentiating your answer.
Initial conditions pin down C: F(x₀)=y₀.
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Try this
Attempt each problem first, then open the worked solution.
1.Find all antiderivatives of 3x²+cos x.