Respuesta :
The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].
Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.
Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.
Then the integral is approximately
[tex]\displaystyle\int_2^{10}f(x)\,\mathrm dx\approx3\cdot2+8\cdot3+15\cdot2+18\cdot1=78[/tex]
so 78.0 is the correct answer.
The 4 subintervals are given: [2, 4], [4, 7], [7, 9], and [9, 10].
Each subinterval has length: 4 - 2 = 2, 7 - 4 = 3, 9 - 7 = 2, and 10 - 9 = 1.
Over each subinterval, we take the value of the function at the right endpoint: 3, 8, 15, and 18.
Then the integral is approximately
∫10 2 f(x) dx=3.2 +8.3=15.2=18.1= 78
so 78.0 is the correct answer.
Riemann sums are approximations of the area under a curve, so they will almost always be slightly more than the actual area (an overestimation) or slightly less than the actual area
What is the difference between Riemann sum and Riemann integral?
Definite integrals represent the exact area under a given curve, and Riemann sums are used to approximate those areas. However, if we take Riemann sums with infinite rectangles of infinitely small width (using limits), we get the exact area, i.e. the definite integral!
What do we use Riemann sums for?
The Riemann sums are used to construct the integral, to define the object. When the functions to be integrated are "nice enough" you have learned a simple formula to compute the integral (involving primitives), but this rule does not define the integral, nor does it allow to compute every integral. Riemann sums help us approximate definite integrals, but they also help us formally define definite integrals.
To learn more about Riemann sums, refer
https://brainly.com/question/104442
#SPJ2
