SME
Calculus II · Problem type
Which integration method?
Use this for “Which method evaluates ∫ x·cos x dx?”
Sort
Look for a product, a factored bottom, a √(a² − x²) or an inside with its derivative.
Tap a card, then tap its group.
Assumptions
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Try u-substitution first: it works when an inside part appears with its derivative, up to a constant.
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By parts, ∫ u dv = uv − ∫ v du, suits a product where u gets simpler when differentiated (LIATE as a rule of thumb).
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Partial fractions split a quotient of polynomials whose bottom factors; trig substitution x = a sin θ removes a √(a² − x²).
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Integration by parts, partial fractions, trig substitution
Main lesson
By parts with a sine: x sin(kx)
Use this for “Evaluate the integral of x sin(2x) from 0 to π/2.”
Partial fractions: two linear factors
Use this for “Evaluate the integral of 1 ÷ ((x − 3)(x + 1)) from 4 to 6.”
Trig substitution: the area under a circle
Use this for “Evaluate the integral of √(9 − x²) from 0 to 2” (r = 3).