Maths WorkshopMaths problems with full solutions

Integration techniques

15 problems · Substitution, integration by parts and linearisation.

Ex.187Integral of sine squared
#integrals #trigonometry
Integration techniques
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Ex.188Integration by parts
#integrals #by parts
Integration techniques
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Ex.374Integration by parts, two classics
#integration by parts #definite integrals
Integration techniques
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Ex.381Simplifying and decomposing rational integrands
#partial fractions #rational functions
Integration techniques
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Ex.386Integration by substitution
#substitution #change of variable
Integration techniques
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Ex.399Trigonometric integrals by linearisation
#trigonometric integrals #linearisation
Integration techniques
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Ex.723A reduction formula
#reduction formula #integration by parts #recurrence
Integration techniques
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Ex.728Completing the square before integrating
#rational functions #completing the square #arctangent
Integration techniques
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Ex.738Integrating by parts twice and coming back
#integration by parts #exponential #trigonometric
Integration techniques
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Ex.763Integrating ln and arctan by parts
#integration by parts #logarithm #arctangent
Integration techniques
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Ex.780The area of an ellipse
#trigonometric substitution #area #ellipse
Integration techniques
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Ex.786Using the substitution x → a + b − x
#symmetry #substitution #trigonometric integrals
Integration techniques
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Ex.1517The tangent half-angle substitution
#Weierstrass substitution #trigonometric integrals #rational functions
Integration techniques
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Ex.1521Wallis integrals
#Wallis integrals #recurrence #asymptotics #pi
Integration techniques
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Ex.2078An integral that equals its own mirror image
#symmetry #substitution #logarithm #tangent
Integration techniques
Olympiad
Olympiad