Definite Integrals

[keen silo]

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[cerulean hinge]

so you know how to do the left points?

[nova hinge]

no not really I am kinda stumped on how to even start the question to be honest

[cerulean hinge]

oh

so you know how we have 4 rectangles right?

[nova hinge]

yup

[cerulean hinge]

so we want to get the change in x

which is delta x

and we have 4 rectangles so thats n

and delta x is (b-a)/n

that is the width of the rectangles

[nova hinge]

b - a / n

[cerulean hinge]

yes

[a,b]

[nova hinge]

so 4-(-4)/ 4

[cerulean hinge]

yes

[nova hinge]

which would give us 2

so how would i be able to find the left endpoints

[cerulean hinge]

for the left end points we basically need to find the difference in that interval

so the change in x is 2

we then slice up the interval into lengths of two

so we have -4, -2, 0, 2, 4 as our endpoints

you get that right?

[nova hinge]

yup

so i would multiply those endpoints

by 2?

or no

[cerulean hinge]

no

we have to find the sum of four of the points and multiply it by the change in x

[nova hinge]

okay

[cerulean hinge]

the left side area is approximately 2(f(-4)+f(-2)+f(0)+f(2))

[nova hinge]

whch would be -8?