![]() ![]() Images/mathematical drawings are created with GeoGebra. ![]() The area of a region is found by breaking it into thin vertical rectangles and applying the lower and the upper limits, the area of the region is summed up. ![]() The area under the curve is defined as the region bounded by the function we’re working with, vertical lines representing the function’s bounds, and the $\boldsymboldx = \ln 5 \approx 1.609$ squared units A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line. If f (x) 0, then the definition essentially is the limit of the sum of the areas of approximating rectangles, so, by design, the definite integral represents the area of the region. b a f (x)dx lim n n i1f (a +ix)x, where x b a n. For now, let’s learn how areas under the curve are represented on the $xy$-plane! What is the area under the curve? Let us look at the definition of a definite integral below. We approximate the actual value of an integral by drawing rectangles. Warm-up on integration and keep your notes on antiderivative formulas and properties nearby. Integral is the representation of the area of a region under a curve. Since this topic is an application of integral calculus, review your knowledge of the definite integral and the fundamental theorem of calculus. A is the total area enclosed by the shape, and is found by evaluating the first integral. dA is a differential bit of area called the element. We do this by slicing the solid into pieces, estimating the volume of each.
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