U-Substitution - Worksheet 8 - 12th Grade
HardApply u-substitution to evaluate integrals (Hard)
27 problems · 25-30 minutes · Skills: integrals, u-substitution, calculus
About This Worksheet
This hard-level worksheet contains 27 problems designed for 12th Grade students practicing integration by substitution (u-sub). Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.
U-substitution is the Chain Rule of integration — it is the first and most important technique for evaluating integrals beyond basic antiderivatives. Recognizing the structure that calls for a substitution is a pattern-recognition skill that extends to more advanced integration techniques.
- Identify a composite function structure within an integrand and choose an appropriate substitution
- Compute the new differential, rewrite the integral, integrate, and back-substitute
- Apply substitution to definite integrals by changing the limits of integration
- Recognize when an extra factor is the derivative of the inner function
- Use u-substitution to integrate trig functions with linear arguments
How to Solve: Worked Example
- Read the problem carefully.
- Identify what is being asked.
- Use what you know to find the answer.
- Check your work.
Answer Key
Frequently Asked Questions
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How do I find worksheets at different difficulty levels?
Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.
What skills does this integrals worksheet cover?
This worksheet focuses on integrals, u-substitution, calculus. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.
Can I use this worksheet in my classroom?
Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.
How many problems are on this worksheet?
This worksheet contains 27 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.