AS Mathematics HomeWork-Learning Page

Teacher:	Prof. JM	Section:	AS Mathematics Grade 11
Date:	Week	Grade	Grade 11

Teacher:

Prof. JM

Section:

AS Mathematics Grade 11

Date:

Week

Grade

Grade 11

Basic Integration

Learning Objectives	Understand the concept of integration as the inverse of differentiation and its applications in calculating areas and volumes. Learn to compute the indefinite integral of polynomial functions and apply integration rules such as power rule and sum rule. Apply integration techniques to solve real-world problems, including finding the area under curves and solving motion-related problems.
	Instruction : Show Detailed Working

Learning Objectives

Understand the concept of integration as the inverse of differentiation and its applications in calculating areas and volumes.
Learn to compute the indefinite integral of polynomial functions and apply integration rules such as power rule and sum rule.
Apply integration techniques to solve real-world problems, including finding the area under curves and solving motion-related problems.

Instruction : Show Detailed Working

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Student Materials: Name:.......................Grade.................... Integration Worksheet: Basic Integration Question 1: Evaluate the integral: \[ \int (3x^2 + 2x) \, dx \] Question 2: Evaluate the integral: \[ \int (5x^4 - 4x^3 + x^2) \, dx \] Question 3: Evaluate the integral: \[ \int (2x^3 - 6x) \, dx \] Question 4: Evaluate the integral: \[ \int (x^5 - 3x^2 + 4) \, dx \] Question 5: Evaluate the integral: \[ \int (7x^2 + 5x + 1) \, dx \] Question 6: Evaluate the integral: \[ \int (4x^3 - x^2 + 2) \, dx \] Question 7: Evaluate the integral: \[ \int (x^2 - 4x + 7) \, dx \] Question 8: Evaluate the integral: \[ \int (3x^3 + x^2 - 2x + 4) \, dx \] Question 9: Evaluate the integral: \[ \int (6x^4 - 2x^3 + 5x) \, dx \] Question 10: Evaluate the integral: \[ \int (x^6 - x^4 + x^2) \, dx \] Answer Keys: Answer 1: \( x^3 + x^2 + C \) Answer 2: \( x^5 - x^4 + \frac{x^3}{3} + C \) Answer 3: \( \frac{x^4}{2} - 3x^2 + C \) Answer 4: \( \frac{x^6}{6} - x^3 + 4x + C \) Answer 5: \( \frac{7x^3}{3} + \frac{5x^2}{2} + x + C \) Answer 6: \( x^4 - \frac{x^3}{3} + 2x + C \) Answer 7: \( \frac{x^3}{3} - 2x^2 + 7x + C \) Answer 8: \( \frac{3x^4}{4} + \frac{x^3}{3} - x^2 + 4x + C \) Answer 9: \( \frac{6x^5}{5} - \frac{x^4}{2} + \frac{5x^2}{2} + C \) Answer 10: \( \frac{x^7}{7} - \frac{x^5}{5} + \frac{x^3}{3} + C \)	Student Materials: Show detailed steps here
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Student Materials:

Name:.......................Grade....................

Integration

Worksheet: Basic Integration

Question 1: Evaluate the integral: \[ \int (3x^2 + 2x) \, dx \]

Question 2: Evaluate the integral: \[ \int (5x^4 - 4x^3 + x^2) \, dx \]

Question 3: Evaluate the integral: \[ \int (2x^3 - 6x) \, dx \]

Question 4: Evaluate the integral: \[ \int (x^5 - 3x^2 + 4) \, dx \]

Question 5: Evaluate the integral: \[ \int (7x^2 + 5x + 1) \, dx \]

Question 6: Evaluate the integral: \[ \int (4x^3 - x^2 + 2) \, dx \]

Question 7: Evaluate the integral: \[ \int (x^2 - 4x + 7) \, dx \]

Question 8: Evaluate the integral: \[ \int (3x^3 + x^2 - 2x + 4) \, dx \]

Question 9: Evaluate the integral: \[ \int (6x^4 - 2x^3 + 5x) \, dx \]

Question 10: Evaluate the integral: \[ \int (x^6 - x^4 + x^2) \, dx \]

Answer Keys:

Answer 1: \( x^3 + x^2 + C \)
Answer 2: \( x^5 - x^4 + \frac{x^3}{3} + C \)
Answer 3: \( \frac{x^4}{2} - 3x^2 + C \)
Answer 4: \( \frac{x^6}{6} - x^3 + 4x + C \)
Answer 5: \( \frac{7x^3}{3} + \frac{5x^2}{2} + x + C \)
Answer 6: \( x^4 - \frac{x^3}{3} + 2x + C \)
Answer 7: \( \frac{x^3}{3} - 2x^2 + 7x + C \)
Answer 8: \( \frac{3x^4}{4} + \frac{x^3}{3} - x^2 + 4x + C \)
Answer 9: \( \frac{6x^5}{5} - \frac{x^4}{2} + \frac{5x^2}{2} + C \)
Answer 10: \( \frac{x^7}{7} - \frac{x^5}{5} + \frac{x^3}{3} + C \)

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