Trigonometric Substitution (Calculus II)
Free printable university Calculus II worksheet: trigonometric substitution for integrands with sqrt(a^2-x^2), sqrt(a^2+x^2) and sqrt(x^2-a^2), with reference-triangle back-substitution. Every answer key is computed and verified by differentiation.
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Calculus II · Math worksheet
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Date
Math
Integration Techniques: Trigonometric Substitution
Match each integrand to its substitution: sqrt(a^2 - x^2) takes x = a sin(theta); a^2 + x^2 or sqrt(a^2 + x^2) takes x = a tan(theta); sqrt(x^2 - a^2) takes x = a sec(theta). Substitute, integrate in theta, then use a reference triangle to return to x. Include + C.
- 1.Evaluate the integral of dx/ using a trigonometric substitution.
- 2.Evaluate the integral of dx using a trigonometric substitution.
- 3.Evaluate the integral of dx/(16 + ) using a trigonometric substitution.
- 4.Evaluate the integral of dx/ using a trigonometric substitution.
- 5.Evaluate the integral of dx/ for x > 5, using a trigonometric substitution.
- 6.Evaluate the integral of / dx using a trigonometric substitution.
- 7.Evaluate the integral of dx/ using a trigonometric substitution.
- 8.Evaluate the integral of dx using a trigonometric substitution.
- 9.Evaluate the integral of dx/(4 + ) using a trigonometric substitution.
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