In calculus, an improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits.
Specifically, an improper integral is a limit of the form
In which one takes a limit in one or the other (or sometimes both) endpoints. (Source: Wikipedia)
Example problems for solve online improper integrals
Online improper integrals example 1:
Solve:
Find the value of the integration function
`lim_(b->0) int_3^b(2x + 3)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->0)` [2 `(x^2 / 2)` + 3x]b3
Substitute the lower and upper limits, we get
= `lim_(b->0)` (b2 - 3b) - (9 + 9)
Substituting the value of b, we get
= (0) - 18
After substituting the limits, we get
= - 18
Answer:
The final answer is - 18
Online improper integrals example 2:
Solve:
Find the value of the integration function
`lim_(b->2) int_0^b(7x^3 + 3x^2)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->2)` [7 `(x^4 / 4)` + 3`(x^3 / 3)` ]b0
Substitute the lower and upper limits, we get
= `lim_(b->2)` [`(7 / 4)` b4 + b3] - (0)
Substituting the value of b, we get
= [(7 / 4) 24 + 23] - 0
After substituting the limits, we get
= 36
Answer:
The final answer is 36
Online improper integrals example 3:
Solve:
Find the value of the integration function
`lim_(b->1) int_2^b(6x^2 + 18x)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->1)` [6 `(x^3 / 3)` + 18 `(x^2 / 2)` ]b2
Substitute the lower and upper limits, we get
= `lim_(b->1)` (2b3 + 9b2) - (16 + 36)
Substituting the value of b, we get
= (11) - 52
After substituting the limits, we get
= - 41
Answer:
The final answer is - 41
Practice problems for solve online improper integrals
Online improper integrals example 1:
Solve:
Find the value of integration of the function
`lim_(b->0) int_5^b(6x)dx`
Answer:
The final answer is - 75
Online improper integrals example 2:
Solve:
Find the value of integration of the function
`lim_(b->6) int_0^b(12x + 2)dx`
Answer:
The final answer is 228
Specifically, an improper integral is a limit of the form
In which one takes a limit in one or the other (or sometimes both) endpoints. (Source: Wikipedia)
Example problems for solve online improper integrals
Online improper integrals example 1:
Solve:
Find the value of the integration function
`lim_(b->0) int_3^b(2x + 3)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->0)` [2 `(x^2 / 2)` + 3x]b3
Substitute the lower and upper limits, we get
= `lim_(b->0)` (b2 - 3b) - (9 + 9)
Substituting the value of b, we get
= (0) - 18
After substituting the limits, we get
= - 18
Answer:
The final answer is - 18
Online improper integrals example 2:
Solve:
Find the value of the integration function
`lim_(b->2) int_0^b(7x^3 + 3x^2)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->2)` [7 `(x^4 / 4)` + 3`(x^3 / 3)` ]b0
Substitute the lower and upper limits, we get
= `lim_(b->2)` [`(7 / 4)` b4 + b3] - (0)
Substituting the value of b, we get
= [(7 / 4) 24 + 23] - 0
After substituting the limits, we get
= 36
Answer:
The final answer is 36
Online improper integrals example 3:
Solve:
Find the value of the integration function
`lim_(b->1) int_2^b(6x^2 + 18x)dx`
Solution:
Integrate the given function with respect to x, we get
= `lim_(b->1)` [6 `(x^3 / 3)` + 18 `(x^2 / 2)` ]b2
Substitute the lower and upper limits, we get
= `lim_(b->1)` (2b3 + 9b2) - (16 + 36)
Substituting the value of b, we get
= (11) - 52
After substituting the limits, we get
= - 41
Answer:
The final answer is - 41
Practice problems for solve online improper integrals
Online improper integrals example 1:
Solve:
Find the value of integration of the function
`lim_(b->0) int_5^b(6x)dx`
Answer:
The final answer is - 75
Online improper integrals example 2:
Solve:
Find the value of integration of the function
`lim_(b->6) int_0^b(12x + 2)dx`
Answer:
The final answer is 228
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