Definite integral examples
[DOC File]Primer On Integration
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The definite integral as the area of a region under the curve, . If is any point in the subinterval, then the sum. ... The following are some more examples of exact integration. You can use the brief table of integrals given in Table 1. Table 1 A brief table of integrals.
[DOCX File]MA-C4 Integral calculus-y12
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Define the definite integral . a b f ( x ) dx for the area under the curve y = f ( x ) from x = a to x = b if f ( x )≥0 Approximate a definite integral by dividing the area into a given number of trapezia with equal widths, calculating the areas of individual trapezia, then the total area.
[DOC File]Integration by Substitution
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The integral above has an important geometric interpretation that you need to keep in mind. Recall that, geometrically, the definite integral represents the area under the curve. Similarly, the integral is a definite integral that represents the area under the curve over the interval as the figure below shows.
[DOC File]Simpson 3/8 Rule for Integration
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The integral shown in Equation (1) can be expressed as (15) Using Simpson 3/8 rule (See Equation 12) into Equation (15), one gets (16) (17) Example 2. The vertical distance in meters covered by a rocket from to seconds is given by. Use Simpson 3/8 multiple segments rule with six segments to estimate the vertical distance. Solution
[DOC File]CALCULUS
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If we specify the limits x = a x = b, we call the integral a definite integral. To solve a definite integral, we first integrate the function as before (i.e. find its indefinite integral), then feed in the 2 values of the limits. Subtracting one from the other gives the area. Example. 1.
[DOC File]Improper Integrals**
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Otherwise, the integral will be divergent. Example 8. Evaluate . The integrand has an infinite discontinuity inside the interval at x = 2, which means that we follow Case 3 and write the integral as the sum of two separate definite integrals. Remember, the integral is convergent because both parts were convergent. The p-test for Convergence of ...
[DOCX File]VOCABULARY: Area, definite integral, Riemann Sum ...
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estimation, infinite Riemann Sums to find exact answers, understand the Use of the Fundamental Theorem as a method of evaluating Definite Integrals, the Fundamental Theorem as a method to find the Derivative of an Integral, the relationship between integrals and derivatives, show how to estimate Areas using the Trapezoidal approximation, how to find the average value of a function, how to ...
[DOC File]LESSON X
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Examples. Determine whether the following improper integrals converge or diverge. If the integral converges, then give its value. ... The integral is improper with an infinite limit of integration and a discontinuity. ... we will use the following property of definite integrals. = + , where c is a real number in the open interval . Since 3 is ...
[DOC File]Indefinite Integrals Calculus
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Compute the following definite integral: Solution: Using the limit definition we found that We now can verify this using the theorem as follows: We first note that is an antiderivative of Hence we have . We conclude the lesson by stating the rules for definite integrals, most of which parallel the rules we stated for the general indefinite ...
[DOC File]Basic Counting - University of Kentucky
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Note that in both these examples the pdf is not a continuous function. Also note that in all these cases the pdf behaves as a linear density function in the physical sense: the definite integral of the density of a nonhomogeneous wire or of a lamina gives the mass of the wire or lamina over the specified interval. Here the mass is the probability.
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