NSW Maths Advanced · Free Worksheet
Integral Calculus — Anti-Differentiation & Areas Under Curves
Anti-differentiation and using definite integrals to find the area under a curve — practice questions for HSC Maths Advanced.
What's inside
- A short recap of the method before the questions start
- Practice questions ordered from easiest to hardest
- Space to show full working, plus an answer key
Preview
Sample questions
Question 1
Find ∫(6x² − 4x + 3) dx.
Show worked solution
Anti-differentiate term by term: ∫6x² dx = 2x³, ∫−4x dx = −2x², ∫3 dx = 3x. So the result is 2x³ − 2x² + 3x + C.
Question 2
Find the area under the curve y = x² between x = 1 and x = 3.
Show worked solution
Area = ∫[1 to 3] x² dx = [x³/3] from 1 to 3 = 27/3 − 1/3 = 26/3, or 8⅔ square units.
Want the full practice library?
Sign up for a free 90-day trial to unlock every NSW Maths Advanced worksheet, past exam papers, interactive tools and more.
Start your free trial