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- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_5%3A_Integration/5.1%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b].
- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Everett)/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q2/01%3A_Integration/1.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.05%3A_Numerical_IntegrationThe Fundamental Theorem of Calculus gives a concrete technique for finding the exact value of a definite integral. That technique is based on computing antiderivatives. Despite the power of this theor...The Fundamental Theorem of Calculus gives a concrete technique for finding the exact value of a definite integral. That technique is based on computing antiderivatives. Despite the power of this theorem, there are still situations where we must approximate the value of the definite integral instead of finding its exact value.
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/Math_140%3A_Calculus_1_(Gaydos)/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_222_Calculus_2/00%3A_Review_of_Integration/0.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_II_(Reed)/05%3A_Integration/5.01%3A_Approximating_AreasIn this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the are...In this section, we develop techniques to approximate the area between a curve, defined by a function f(x), and the x-axis on a closed interval [a,b]. Like Archimedes, we first approximate the area under the curve using shapes of known area (namely, rectangles). By using smaller and smaller rectangles, we get closer and closer approximations to the area. Taking a limit allows us to calculate the exact area under the curve.
