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Integration can be used to calculate areas. In simple cases, the area is given by a single definite integral. But sometimes the integral gives a negative answer which is minus the area, and in more complicated cases the correct answer can be obtained only by splitting the area into several parts and adding or subtracting the appropriate integrals.
Integrals of Exponential and Logarithmic Functions. ∫ ln x dx = x ln x − x + C. + 1 x. + 1. x ∫ x ln xdx = ln x − + C. 2 + 1 ( n + 1 ) x dx = e x + C ∫.
Calculus: Integrals, Area, and Volume. Notes, Examples, Formulas, and Practice Test (with solutions) Topics include definite integrals, area, “disc method”, volume of a solid from rotation, and more.
Finding areas by integration. Integration can be used to calculate areas. In simple cases, the area is given by a single definite integral. But sometimes the integral gives a negative answer which is minus the area, and in more complicated cases the correct answer can be obtained only by splitting the area into several parts and adding or ...
In practice, definite integrals (and areas) are evaluated using the following deep result, which is at the heart of calculus, relating di˙erential and integral calculi, or else tangent line and area computation.
Find the area between the graphs of y = tan-'(2s) and y = x. A graphing calculator shows that these curves intersect near (1.2,1.2) and (-1.2, -1.2). The plan is
Definite integrals are used to solve various problems. One of the usual applications is the calculation of the area of a plane region bounded by curves. This chapter presents different types of regions and gives the methods to calculate their areas.
