Antiderivatives - Worksheet 9 - 12th Grade
HardFind antiderivatives using basic integration rules (Hard)
27 problems · 20-25 minutes · Skills: integrals, antiderivatives, calculus
About This Worksheet
This hard-level worksheet contains 27 problems designed for 12th Grade students practicing antiderivatives & indefinite integrals. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.
Antidifferentiation is the reverse of differentiation and is the first step in the study of integration. Finding antiderivatives directly enables solving differential equations — equations that model how quantities change over time — which are the primary mathematical tool in physics, engineering, and mathematical biology.
- Find antiderivatives of power functions using the reverse Power Rule
- Find antiderivatives of exponential, sine, and cosine functions
- Apply the constant of integration and find specific antiderivatives given initial conditions
- Solve simple differential equations of the form dy/dx = f(x) by antidifferentiation
- Reconstruct a position function from a velocity function and an initial position
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
How do I download this antiderivatives - worksheet 9 worksheet?
Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.
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, antiderivatives, 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 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.