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Calculus Integrals Worksheets

Antiderivatives, definite integrals and average value, substitution, area between curves, and Riemann sums. Every sheet comes with a computed answer key.

Make a mixed integrals sheet
Indefinite integrals (antiderivatives)∫(5x3 − 9x2 − 5) dxFind antiderivatives of polynomials and powers with the reverse power rule, adding the constant of integration.Definite integrals∫21 (3x2 − 2x − 5) dxEvaluate definite integrals of polynomials with the Fundamental Theorem of Calculus, and find the average value of a function on an interval.Integration by substitution∫2x(x2 − 8)5 dxIntegrate powers of a linear or quadratic expression by substituting u for the inside and adjusting for du.Area between curvesy = x2 − 5x + 10, y = x + 2Find where a parabola and a line meet, then integrate the top function minus the bottom one between those points.Riemann sums and the trapezoidal ruleApproximate the area under f(x) = x2 + 3 from x = 0 to x = 4 with 4 strips, using a midpoint sum.Approximate the area under a curve with left, right and midpoint Riemann sums and with the trapezoidal rule.
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