Mathematics · Grades 11–12
Integrate a linear function
Evaluate the antiderivative at the upper limit minus the lower limit.
The key idea
Evaluate the antiderivative at the upper limit minus the lower limit.
∫(ax + b) dx = ax²/2 + bx + C
Worked examples
Evaluate the definite integral of (22x + 8) from x = 1 to x = 9.
F(9) − F(1) = 944; F(x) = 11x² + 8x
944
Evaluate the definite integral of (14x + 11) from x = 4 to x = 9.
F(9) − F(4) = 510; F(x) = 7x² + 11x
510
Try it yourself
Evaluate the definite integral of (6x + 14) from x = 0 to x = 1.
Evaluate the definite integral of (10x + 15) from x = 0 to x = 7.
Check your understanding
Answers and marking notes
- 17
F(1) − F(0) = 17; F(x) = 3x² + 14x
- 350
F(7) − F(0) = 350; F(x) = 5x² + 15x
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.