High School Calculus/Evaluating Definite Integrals

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Evaluating a Definite Integral[edit]

Let's say you have the parabola x^2 and you want to find the area from x=2 to x=4

2 \leq A \leq 4


In order to take the integral of the function you have to do the opposite that of the derivative

The power of the variable x will have a number added to it. So, x^{(a+1)}

then the number gets inverted and brought out front.

\frac{1}{a+1} * x^{(a+1)}

\int_{2}^{4}x^{2}\, dx

From here we integrate and plug (b) into the indefinite integral and subtract the integral from (a) plugged into the indefinite integral.


Now we evaluate the integral





is the area underneath the curve from 2 to 4. In other words 2 \leq A \leq 4