# Stewart â€“ Calculus â€“ 5.1 / 5.2 â€“ Areas and Distances / The Definite Integral

Approximating Area Using Rectangles
httpv://youtu.be/vqSPGeYO2UA

The Definite Integral
httpv://youtu.be/ODwkTt0RMDg

Calculating a Definite Integral Using Riemann Sums â€” Part 1
httpv://youtu.be/gFpHHTxsDkI

Calculating a Definite Integral Using Riemann Sums â€” Part 2
httpv://youtu.be/GE4OLfmJ8P8

Three equations that give formulas for sums of powers of positive integers:

These formulas are simple rules for working with sigma notation:

Use the form of the definition of the integral

to evaluate the integral.
$\int_{1}^{2} x^3 dx$

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