Anti Derivative Word Problems
Introduction to anti derivatives word problems:
Anti derivative is one of the prominent part of calculus. Anti derivatives are also known as integration. Integration of the function f(x) is denoted as F(x). Word problems are also used in anti derivatives. The anti derivatives problems are mostly use the formulas. It has constant value in their result. Different types of word problems are used in anti derivative calculus. Now in this article we solve some problems related to anti derivative word problems.
Example Problems for Anti Derivative Word Problems
Anti derivative word problems - example problem 1:
The acceleration of the given function is A = 4t2 - 8t. Find the velocity function V using anti derivative formula.
Solution:
Given acceleration function is A = 4t2 - 8t
For finding velocity function V, we have to find the anti derivative of the acceleration function
Integrate the given acceleration function, we get
'V = 4 (t^3/3) - 8 (t^2/2) + c'
After rearranging, we get
' V = (4/3)t^3 - 4t^2 + c'
Answer:
The final answer is 'V = (4/3)t^3 - 4t^2 + c'
Anti derivative word problems - example problem 2:
The acceleration of the given function is A = 30t2 + 16t - 4. Find the velocity function V using anti derivative formula.
Solution:
Given acceleration function is A = 30t2 + 16t - 4
For finding velocity function V, we have to find the anti derivative of the acceleration function
Integrate the given acceleration function, we get
' V = 30 (t^3/3) + 16 (t^2/2) - 4t + c'
After rearranging, we get
'V = 10t^3 + 8t^2 - 4t + ' c
Answer:
The final answer is 'V = 10t^3 + 8t^2 - 4t + c'
Anti Derivative Word Problems - Example Problem 3:
The acceleration of the given function is A = 10t4 + 40t3 - 72. Find the velocity function V using anti derivative formula.
Solution:
Given acceleration function is A = 10t4 + 32t3 - 72
For finding velocity function V, we have to find the anti derivative of the acceleration function
Integrate the given acceleration function, we get
'V = 10 (t^5/5) + 32 (t^4/4) - 72t + c'
After rearranging, we get
' V = 2t^5 + 8t^4 - 72t + c'
Answer:
The final answer is 'V = 2t^5 + 8t^4 - 72t + c'
by: jeri
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