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Definite Integral as a Signed Area

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Explanations 1

We think of areas as positive, but when using integrals to calculate areas, they can be negative. When an area is negative, it means it is below the xxx-axis. Consider y=2x−5y =…
By Vincent Huang, Stephen Sacchetti, Moor Xu

Problems 3

Find ∫−11∣x∣ dx\int_{-1}^1 |x| \,dx∫−11∣x∣dx by interpreting the integral as a (possibly signed) area.
Find ∫02x dx\int_0^2 x\,dx∫02xdx by interpreting the integral as a (possibly signed) area.
Find ∫−11x dx\int_{-1}^1 x \,dx∫−11xdx by interpreting the integral as a (possibly signed) area.