Quick question on integral calculation

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SUMMARY

The discussion centers on calculating the integral of a function f, specifically finding f(π/2) given the area under the curve from x=0 to x=a as a² + (a/2)sin(a) + (π/2)cos(a). The user correctly identifies that the antiderivative F(a) - F(0) equals the provided expression, but encounters a discrepancy when substituting a=0, resulting in 0 on the left and π/2 on the right. The consensus is that either the problem statement is incorrect or the user misinterpreted the question.

PREREQUISITES
  • Understanding of integral calculus and antiderivatives.
  • Familiarity with the Fundamental Theorem of Calculus.
  • Knowledge of limits and continuity in functions.
  • Ability to differentiate and manipulate trigonometric functions.
NEXT STEPS
  • Review the Fundamental Theorem of Calculus for clarity on antiderivatives.
  • Practice solving integrals involving trigonometric functions and limits.
  • Examine examples of continuity and differentiability in calculus.
  • Consult additional resources on common pitfalls in integral calculations.
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Students studying calculus, educators teaching integral calculus, and anyone seeking to clarify concepts related to antiderivatives and area under curves.

matts0
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Homework Statement


Hello, I have a question from my textbook on integral calculation. It's
Find f(pi/2) from the following information.
(i) f is positive and continuous.
(ii) the area under the curve y=f(x) from x=0 to x=a is a2+(a/2)*sin(a)+(π/2 )*cosa

So I think the second condition implies
F(a)-F(0) = a2+(a/2)*sin(a)+(π/2 )*cosa (F is the antiderivate of f)
But if I let a=0, I find the lefthand side of the equation will be 0 but the righthand side will be π/2 .
So please someone tell me where I made a mistake which seems to be quite a silly one.
Thanks in advance.

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
Did you calculate the derivative?
 
Either you copied the question incorrectly or else the book has written an incorrect question. You are right: the two sides are different in the limit a-->0.

RGV
 

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