Basic Calculus: Antidifferentiation Rules
Basic Calculus - Antidifferentiation Rules
Flashcards (5) Click to reveal answers
Card #1
Front (Question/Term)
∫ 7dx
Back (Answer/Definition) ANSWER
1. The integral of dx alone is:
∫ dx=x
2. The number 7 is a constant, so it
stays in front of the integral.
3. Multiply the constant by the result: 7x
4. Always add the constant of
integration C
Final Answer:
7x + C
Card #2
Front (Question/Term)
∫ x⁴dx
Back (Answer/Definition) ANSWER
Step-by-step solution (Power Rule):
1. Identify the exponent: x⁴
2. Add 1 to the exponent: 4+1=5
3. Divide by the new exponent:
x⁵/5
4. Add + C to the final answer.
x⁵/5 + C
Card #3
Front (Question/Term)
∫ (3x+4)dx
Back (Answer/Definition) ANSWER
1. Separate the integral:
∫ 3x²dx + ∫ 4dx
2. Integrate each term separately:
• ∫ 3x²dx=3 • x³/3 = x³
3. Combine results and add + C to the final answer.
x³ + 4x + C
Card #4
Front (Question/Term)
∫ cos x dx
Back (Answer/Definition) ANSWER
1. Recall basic antiderivatives:
- The derivative of sin x is cos x
2. Since antidifferentiation is the reverse
of differentiation:
∫ cosx dx = sinx
3. Add + C to the final answer:
sinx + C
Card #5
Front (Question/Term)
∫ 2x(1+x²)dx
Back (Answer/Definition) ANSWER
Step-by-step solution (Substitution
Method):
1. Let:
u=1 + x²
2. Differentiate both sides:
du = 2x dx
3. Substitute into the integral:
∫ u du
4. Integrate:
u²/2
5. Substitute back u=1+x²
(1 + x²)²/2 + C
5
Total Cards0
Revealed5
HiddenStudy Information
Set Details
- Subject: Basic Calculus
- Topic: Antidifferentiation Rules
- Difficulty: Easy
- Created: Jan 29, 2026
- Last Updated: Jan 29, 2026
Study Controls
Study Tips
- Try to recall the answer before clicking
- Click the card to test your knowledge
- Use "Reveal All" for quick review
- Study in short, frequent sessions
- Check hints when you get stuck