In this section, you'll do some basic integration problems. These problems will only involve elementary algebra and the application of basic rules of integration. These problems will not require u-substitution or integration by parts. Before attempting this section, you should be very good at performing elementary algebra, you should know your trig identities, and you should know basic integral identities, such as the reverse power rule.
Basic integration problems
\(\displaystyle \int \left(1 + 2x - 4x^3\right)\,dx\)
\(x + x^2 - x^4 + C\)
\(\displaystyle \int \dfrac{3x - 2}{\sqrt{x}}\,dx\)
\(2x^{3 / 2} - 4x^{1 / 2} + C\)
\(\displaystyle \int \dfrac{\sin \theta + \sin \theta\tan^2 \theta}{\sec^2 \theta}\,d\theta\)
\(-\cos \theta + C\)
\(\displaystyle \int (x + 1)\left(x^2 + 3\right)\,dx\)
\(\dfrac{x^4}{4} + \dfrac{3x^2}{2} + \dfrac{x^3}{3} + 3x + C\)
\(\displaystyle\int x^2(3x - 1)\ dx\)
\(\dfrac{3x^4}{4} - \dfrac{x^3}{3} + C\)
\(\displaystyle\int \dfrac{x^3 + 3x^2 - 5}{x^2}\ dx\)
\(\dfrac{x^2}{2} + 3x + 5x^{-1} + C\)
\(\displaystyle\int \sqrt[3]{x^5}\ dx\)
\(\dfrac{3}{8}x^{8 / 3} + C\)
Conclude by giving your students these challenges:
- 2017 Math Kangaroo Levels 3-4 Problem #19 by STEM4all
- More Children and Plants by NRICH
- Three Four Five by NRICH
- Going to the Cinema by NRICH
- A Curious Surface Area