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- Each integrand is top-heavy.\displaystyle\int \dfrac{x^2 - 3x + 5}{x - 1}\,dx\displaystyle\int \dfrac{4x - 7}{2x + 1}\,dx\displaystyle\int \dfrac{x^2}{x^2 + 16}\,dx\displaystyle\int \dfrac{2x^3 - x^2 + 21x + 4}{x^2 + 9}\,dx
- Evaluate _0² 2x² + 7x - 12x + 1\,dx.
- Find the function f with $f'
- Evaluate _0³ x^4 + x² + 3x² + 3\,dx exactly.
- Zoe finds an antiderivative by integrating the top and the bottom separately.
- Mateo runs a packet-filling machine at a seed company.
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Dividing before integrating: the lesson ›More Chapter 8 worksheets: The fundamental theorem and antiderivatives
- 8.1The first fundamental theorem of calculus
- 8.2Graphing an accumulation function
- 8.3Antiderivatives and indefinite integrals
- 8.4The second fundamental theorem of calculus
- 8.5Antiderivatives of trig, exponential and log functions
- 8.6u-substitution
- 8.7Dividing before integrating
- 8.8Completing the square inside an integral
- 8.9Differential equations and their solutions