Integration Definitions, Properties & Theorems
Integration Definitions, Properties & Theorems

Integration Definitions, Properties & Theorems

Lead Author(s): Kelly Cline

Student Price: FREE

These questions explore integration defined through Riemann sums, as well as basic properties and theorems of integrals

[Theorems] 1

If f(x)=1xt4dt f(x) = \int_1^x t^4 dt , then

A

f(x)=t4 f ’ (x) = t^4

B

f(x)=x4 f ’ (x) = x^4

C

f(x)=15x515 f ’ (x) = \frac{1}{5} x^5 – \frac{1}{5}

D

f(x)=x41 f ’ (x) = x^4 – 1

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[Riemann sums] 1

TrueorFalse:\bf{True or False:} If a piece of string has been chopped into nn small pieces and the ithi^{th} piece is Δxi\Delta x_i inches long, then the total length of the string is exactly i=1nΔxi\sum_{i=1}^n \Delta x_i .

A

True, and I am very confident

B

True, but I am not very confident

C

False, but I am not very confident

D

False, and I am very confident

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