Finding a Specific Antiderivative (solving for C) (Year 11-12)
Free printable Year 11-12 Mathematical Methods worksheet: finding f(x) from f'(x) and a point on the curve by solving for the constant of integration.
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Year 11-12 · Math worksheet
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Math
Integration: Finding a Specific Antiderivative (solving for C)
Each curve has the given gradient function f'(x) and passes through the stated point. Antidifferentiate, then substitute the point to find the constant of integration C, and write f(x).
- 1.The gradient function of a curve is f'(x) = 2x - 1, and the curve passes through the point (-1, 7). Find f(x).
- 2.The gradient function of a curve is f'(x) = - - 4x^2 - 3x + 2, and the curve passes through the point (-3, 2). Find f(x).
- 3.The gradient function of a curve is f'(x) = -4x + 3, and the curve passes through the point (1, -6). Find f(x).
- 4.The gradient function of a curve is f'(x) = -x - 4, and the curve passes through the point (4, 5). Find f(x).
- 5.The gradient function of a curve is f'(x) = 5x^2 + 5x, and the curve passes through the point (3, -2). Find f(x).
- 6.The gradient function of a curve is f'(x) = -5x^2 - 6x + 6, and the curve passes through the point (-2, 1). Find f(x).
- 7.The gradient function of a curve is f'(x) = -6x^2 - 4x + 5, and the curve passes through the point (0, -3). Find f(x).
- 8.The gradient function of a curve is f'(x) = 4x^3 - 5x^2 + x - 2, and the curve passes through the point (0, -1). Find f(x).
- 9.The gradient function of a curve is f'(x) = -x + 1, and the curve passes through the point (4, 5). Find f(x).
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About this worksheet
In class: First antidifferentiate to get the family f(x) = F(x) + C, then use the given point: substitute its coordinates to make an equation in C and solve. Emphasise that the point pins down one member of the family of parallel curves.
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.