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- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Kravets)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_(Open_Stax)_Novick/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/Southwestern_College/Business_Calculus/04%3A_Unit_4_-_Integration/4.03%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
- https://math.libretexts.org/Courses/College_of_Southern_Nevada/Calculus_(Hutchinson)/05%3A_Integration/5.03%3A_The_Definite_Integralthe area between a function and the x-axis such that the area below the x-axis is subtracted from the area above the x-axis; the result is the same as the definite integral of the function...the area between a function and the x-axis such that the area below the x-axis is subtracted from the area above the x-axis; the result is the same as the definite integral of the function total area between a function and the x-axis is calculated by adding the area above the x-axis and the area below the x-axis; the result is the same as the definite integral of the absolute value of the function
- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/05%3A_Integration/5.02%3A_The_Definite_IntegralIf f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exi...If f(x) is a function defined on an interval [a,b], the definite integral of f from a to b is given by ∫baf(x)dx=limn→∞n∑i=1f(x∗i)Δx, provided the limit exists. If this limit exists, the function f(x) is said to be integrable on [a,b], or is an integrable function. The numbers a and b are called the limits of integration; specifically, a is the lower limit and b is the upper limit. The function f(x) is the integrand, and x is the variable of integration.
