**High School Number Sense Lesson 88: Integrals**

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.

**For example:**

**The integral of a constant A is Ax,**

The integral of x is x

The integral of x

The integral of x

The integral of x is x

^{2}/2 or 1/2 x^{2},The integral of x

^{2}is x^{3}/3 or 1/3 x^{3},The integral of x

^{3}is x^{4}/4 or 1/4 x^{4}, etc.**To solve an integral problem:**

- 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

**Examples in the PDF below.**

integral_examples.pdf |

**Up Next for High School: Mult5**