A definite integral is an integralwith upper and lower limits. If is restricted to lie on the real line, the definite integral is known as a Riemann integral (which is the usual definition encountered in elementary textbooks). However, a general definite integral is taken in the complex plane, resulting in the contour integral
with , , and in general being complex numbers and the path of integration from to known as a contour.
The first fundamental theorem of calculus allows definite integrals to be computed in terms of indefinite integrals, since if is the indefinite integral for a continuous function , then
This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral. Definite integrals may be evaluated in the Wolfram Language using Integrate[f, x, a, b].
The question of which definite integrals can be expressed in terms of elementary functions is not susceptible to any established theory. In fact, the problem belongs to transcendence theory, which appears to be "infinitely hard." For example, there are definite integrals that are equal to the Euler-Mascheroni constant . However, the problem of deciding whether can be expressed in terms of the values at rational values of elementary functions involves the decision as to whether is rational or algebraic, which is not known.
9514 1404 393
Answer:
(b) 3h^-8·k^10
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
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Answer:
2x + 15 = 37 - 2
Step-by-step explanation:
we know his age is the variable x
so (Two times his age plus fifteen equals thirty seven minus two) turns into:
2x (plus fifteen equals thirty seven minus two)
plus fifteen is +15 so now we have:
2x + 15 (equals thirty seven minus two)
equals is =, so now we have:
2x + 15 = (thirty seven minus two)
thirty seven is 37, so now we have:
2x + 15 = 37 (minus two)
minus two is -2, so now we have:
2x + 15 = 37 - 2
Answer:
8530
Step-by-step explanation:
The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530
The 95% C.I will be given as follows:
mean=199
standard deviation=16.5
n=12
thus:
value of z corresponding to 95% is 1.96, thus the 95% C.I will be found as follows:
μ+/-z(σ/√n)
thus plugging in the values we get:
199+/-1.96(16.5/√12)
=199+/-9.3358
Answer: 199-9.3358≤x≤199+9.3358