Integration

Integration as reverse differentiation, including indefinite and definite integrals, substitution and integration by parts, partial fractions, applications to area, volume and motion, and use of GDC to evaluate definite integrals.

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Definite Integrals, Areas, and Basic Anti-Derivatives

Integration

Evaluating definite integrals \(\int_a^b f\left(x\right)\,dx=F\left(b\right)-F\left(a\right)\), using anti-derivatives \(\int f\left(x\right)\,dx=F\left(x\right)+C\) and the power rule \(\int x^n dx=\frac{x^{n+1}}{n+1}+C\) for \(n\neq -1\), with linearity, splitting or combining intervals, boundary conditions, and finding areas under a curve, between a curve and the \(x\)-axis, or between two curves using \(\left|f\left(x\right)\right|\) and \(\left|f\left(x\right)-g\left(x\right)\right|\).

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Anti-Derivative Rules

Integration

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Techniques of Integration

Integration

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Kinematics

Integration

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Volumes of Revolution

Integration

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Integration

Integration as reverse differentiation, including indefinite and definite integrals, substitution and integration by parts, partial fractions, applications to area, volume and motion, and use of GDC to evaluate definite integrals.