Evaluate the integral. \int_{2}^{3}[3x^{2}+2x+\frac{1}{x^{2}}]dx

druczekq4 2021-11-20 Answered
Evaluate the integral.
23[3x2+2x+1x2]dx
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

breisgaoyz
Answered 2021-11-21 Author has 14 answers
Step 1
The given integral is 23[3x2+2x+1x2]dx.
Step 2
Evaluate the given integral as shown below:
23[3x2+2x+1x2]dx=23[3x2]dx+23[2x]dx+23[1x2]dx
=323x2dx+223xdx+23x2dx
=3[x33]23+2[x22]23+[x11]23
=[x3]23+[x2]23[1x]23
=[278]+[94][1312]
=[19]+[5]+[16]
=1456
Not exactly what you’re looking for?
Ask My Question
Rosemary McBride
Answered 2021-11-22 Author has 10 answers
Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
abf(x)dx=F(x)ab=F(b)F(a)
Step 2: In this case, f(x)=(3x2+2x+1x2). Find its integral.
x3+x21x23
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(3)-F(2):
(33+3213)(23+2212)
Step 4: Simplify.
1456
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-11-07
Use a symbolic integration utility to find the indefinite integral.
(4t3)2dt
asked 2022-07-21
Using the Euler's method (with h = 10 n ) to find y ( 1 )
y = sin ( x ) x
Since
y ( x ) = sin ( x ) x
then
f ( x , y ) = sin ( x ) x
I know
y n + 1 = y n + h f ( x n , y n )
and given y ( 0 ) = 0, so
x 0 = y 0 = 0
Therefore,
x 1 = x 0 + h = 0 + 10 0 = 1 y 1 = y ( x 1 ) = y ( 1 )
Then,
y 1 = 0 + 10 0 f ( x 0 , y 0 )
y 1 = f ( 0 , 0 )
But
f ( 0 , 0 ) = sin ( 0 ) 0 = 0 0
How am I supposed to do it?
asked 2022-04-18

Determine the coordinates of the centriod of the region bounded by the graphs f x =4 -x^2 and g(x) =x + 2

asked 2022-06-22
Why does the integral of 1 a 2 x 2 have 2 different answers for the same domain
asked 2022-08-07
Find the standard form of the equation of the circle having the following properties.
Center at the point (8,-6) Tangent to the x-axis
type the standard form of the equation of this circle
asked 2021-05-23
Use a change of variables to evaluate the following integral.
(cos7x5cos5xcosx)sinxdx
asked 2022-05-08
How can we use Euler's method to approximate the solutions for the following IVP below:
y = y + t y 1 / 2 ,  with  1 t 2 ,   y ( 1 ) = 2 ,
and with h = 0.5
The main concern is the organization, i.e., set up of it for this particular example.

And, if the actual solution to the IVP above is:
y ( t ) = ( t 2 + 2 e e t / 2 ) 2
then, how to compare the actual error and compare the error bound?

New questions