Understanding integrals is...integral...to the success of an advanced number sense student. These problems showed up on the vast majority of high school tests (17 times this year), but not until late on the test. Their median placement is question # 78.
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An integral is the inverse function of differentiation, which we covered in detail in FunctionDeriv. So for each term in an integral problem, perform the opposite operation (or antiderivative):
- Multiply each term by x, and
- Divide by the new exponent of x.
- Take the integral (or antiderivative) of each term in the function to form a new function
- Plug the value at the top of the integral sign into the function
- Plug the value at the bottom of the integral sign into the function
- Subtract the result in Step 3 from the result in Step 2