Antidifferentiation (the Power Rule) (Year 11-12)
Free printable Year 11-12 Mathematical Methods worksheet: antidifferentiation as the reverse of differentiation, using the power rule for indefinite integrals.
✓ Answer key checked by math, never wrong
Year 11-12 · Math worksheet
Name
Date
Math
Integration: Antidifferentiation (the Power Rule)
Find each indefinite integral by reversing differentiation: integral of a x^n dx = a/(n+1) x^(n+1) + C (n not equal to -1). Remember to add + C.
- 1.Find the indefinite integral (antiderivative) of f(x) = -8x^4 with respect to x. Include the constant of integration + C.
- 2.Find the indefinite integral (antiderivative) of f(x) = -5x^4 with respect to x. Include the constant of integration + C.
- 3.Find the indefinite integral (antiderivative) of f(x) = -4x with respect to x. Include the constant of integration + C.
- 4.Find the indefinite integral (antiderivative) of f(x) = 6x^2 + 4x - 6 with respect to x. Include the constant of integration + C.
- 5.Find the indefinite integral (antiderivative) of f(x) = 5x with respect to x. Include the constant of integration + C.
- 6.Find the indefinite integral (antiderivative) of f(x) = + 4x^2 - 2x + 5 with respect to x. Include the constant of integration + C.
- 7.Find the indefinite integral (antiderivative) of f(x) = 6x^2 - 2x - 4 with respect to x. Include the constant of integration + C.
- 8.Find the indefinite integral (antiderivative) of f(x) = 6x^3 + 2x^2 + 6x - 1 with respect to x. Include the constant of integration + C.
- 9.Find the indefinite integral (antiderivative) of f(x) = 6x^3 - 3x^2 - 5 with respect to x. Include the constant of integration + C.
- 10.Find the indefinite integral (antiderivative) of f(x) = 3x + 1 with respect to x. Include the constant of integration + C.
Made with ChalkBee · chalkbee.com
About this worksheet
In class: Anchor it as differentiation run backwards: since d/dx(x^(n+1)) = (n+1)x^n, reversing gives integral of x^n dx = x^(n+1)/(n+1). Raise the power by one, divide by the new power, then always add + C. Check each answer by differentiating it back to the original.
This Year 11-12 math set is free to print or save as a PDF, and its answer key is computed in code, so it is never wrong.