Practice Question: Trig Sub (w/ completing the square)

Trig Sub

4 Activities

Find ∫1x2−2x−3  ⁣dx{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}∫x2−2x−3​1​ dx.

ln⁡∣(x−1)2−42∣+C\ln\left|\frac{\sqrt{\left(x-1\right)^2-4}}{2}\right|+Cln​2(x−1)2−4​​​+C

ln⁡∣x−12+(x−1)2−42∣+C\ln\left|\frac{x-1}{2}+\frac{\sqrt{\left(x-1\right)^2-4}}{2}\right|+Cln​2x−1​+2(x−1)2−4​​​+C

ln⁡∣x−12∣+C\ln\left|\frac{x-1}{2}\right|+Cln​2x−1​​+C

ln⁡∣x−12+(x−1)2−42∣+C\ln\left|\frac{\sqrt{x-1}}{2}+\frac{\left(x-1\right)^2-4}{2}\right|+Cln​2x−1​​+2(x−1)2−4​​+C

ln⁡∣(x−1)2−42∣+C\ln\left|\frac{\left(x-1\right)^2-4}{2}\right|+Cln​2(x−1)2−4​​+C

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Practice: Trig Sub

Evaluate ∫01x4−x2dx\displaystyle\int_0^1\frac{x}{\sqrt{4-x^2}}dx∫01​4−x2​x​dx
*You can technically use a u-substitution for this question, but try to use trig sub for additional practice

Practice: Trig Sub

Practice: Trig Sub
Evaluate ∫01x4−x2dx\displaystyle\int_0^1\frac{x}{\sqrt{4-x^2}}dx∫01​4−x2​x​dx
*You can technically use a u-substitution for this question, but try to use trig sub for additional practice

Practice Question: Trig Sub (w/ completing the square)

Find ∫1x2−2x−3  ⁣dx{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}∫x2−2x−3​1​ dx.

Practice: Trig Sub

Practice: Trig Sub
Evaluate ∫01x4−x2dx\displaystyle\int_0^1\frac{x}{\sqrt{4-x^2}}dx∫01​4−x2​x​dx
*You can technically use a u-substitution for this question, but try to use trig sub for additional practice

Practice Question: Trig Sub (w/ completing the square)

Practice Question
Find ∫1x2−2x−3  ⁣dx{\displaystyle\int}\frac{1}{\sqrt{x^2-2x-3}}\de{x}∫x2−2x−3​1​ dx.

Practice Question: Trig Sub (w/ completing the square)

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Practice: Trig Sub

Practice: Trig Sub

Practice Question: Trig Sub (w/ completing the square)

Practice: Trig Sub

Practice Question: Trig Sub (w/ completing the square)