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Interpreting the behavior of accumulation functions involving area

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Interpreting the behavior of accumulation functions

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Applying properties of definite integrals

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Negative definite integrals

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Finding definite integrals using area formulas

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Definite integral over a single point

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Integrating scaled version of function

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Switching bounds of definite integral

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Integrating sums of functions

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Worked examples: Finding definite integrals using algebraic properties

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Definite integrals on adjacent intervals

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Worked example: Breaking up the integral’s interval

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Worked example: Merging definite integrals over adjacent intervals

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Functions defined by integrals: switched interval

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Finding derivative with fundamental theorem of calculus: x is on lower bound

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Finding derivative with fundamental theorem of calculus: x is on both bounds

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The fundamental theorem of calculus and definite integrals

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The fundamental theorem of calculus and definite integrals

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Antiderivatives and indefinite integrals

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Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule

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Reverse power rule

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Indefinite integrals : sum & multiples

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Rewriting before integrating

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Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals

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Indefinite integral of 1/x

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Indefinite integrals of sin(x), cos(x), and eˣ

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Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals

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Definite integrals: reverse power rule

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Definite integral of rational function

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Definite integral of radical function

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Definite integral of trig function

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Definite integral involving natural log

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Definite integral of piecewise function

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Definite integral of absolute value function

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Integrating using substitution

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𝘶-substitution intro

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𝘶-substitution: multiplying by a constant

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𝘶-substitution: defining 𝘶

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𝘶-substitution: defining 𝘶 (more examples)

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𝘶-substitution: rational function

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𝘶-substitution: logarithmic function

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𝘶-substitution: definite integrals

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𝘶-substitution: definite integral of exponential function

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Integrating functions using long division and completing the square

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Integration using long division

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Integration using completing the square and the derivative of arctan(x)

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Using integration by parts

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Integration by parts intro

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Integration by parts: ∫x⋅cos(x)dx

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Integration by parts: ∫ln(x)dx

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Integration by parts: ∫x²⋅𝑒ˣdx

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Integration by parts: ∫𝑒ˣ⋅cos(x)dx

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Integration by parts: definite integrals

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Integrating using linear partial fractions

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Integration with partial fractions

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Evaluating improper integrals

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Introduction to improper integrals

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Divergent improper integral

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Optional videos

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Proof of fundamental theorem of calculus

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Intuition for second part of fundamental theorem of calculus

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Modeling situations with differential equations

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Differential equations introduction

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Writing a differential equation

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Verifying solutions for differential equations

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Verifying solutions to differential equations

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Sketching slope fields

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Slope fields introduction

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Worked example: equation from slope field

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Worked example: slope field from equation

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Worked example: forming a slope field

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Reasoning using slope fields

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Approximating solution curves in slope fields

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Worked example: range of solution curve from slope field (Opens a modal)

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Approximating solutions using Euler’s method

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Euler’s method

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Worked example: Euler’s method