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Definition of Integral. Riemann Sum. Sum given by the formula. Integral. If f is defined on the interval [ a, b] and the limit exists, then this limit is called the definite integral of f from a to b . f(x) is called the integrand a is the lower limit b is the upp er limit.

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Definition of Integral

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Definition of integral

Definition of Integral


Riemann sum

Riemann Sum

Sum given by the formula


Integral

Integral

If f is defined on the interval [ a, b] and the limit

exists, then this limit is called the definite integral of f from a to b


Definition of integral

f(x) is called the integrand

a is the lower limit

b is the upper limit


Example

Example

Express the Riemann sum below as an integral on the interval [ 0, π ]


Example1

Example

Evaluate the integrals below


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