Integrate sin(x)dx: Typo in Calc Book

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SUMMARY

The discussion centers on the integration of the definite integral ∫sin(x)dx from 0 to π. The correct anti-derivative is identified as -cos(x), leading to F(π) = 1 and F(0) = -1. The calculated result of F(π) - F(0) yields 2, which clarifies the discrepancy with the textbook answer. The confusion arises from an initial miscalculation of F(0).

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  • Knowledge of anti-derivatives
  • Basic trigonometric functions and their properties
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Homework Statement



Integrate the definite integral ∫sin(x)dx given b = ∏ and a = 0.

Homework Equations



Fundamental theorem of calculus; definite integral = F(b) - F(a)

The Attempt at a Solution



The anti-derivative is -cos(x).

F(∏) = -(-1) = 1.
F(0) = 1.
F(b) - F(a) = 0.

Why does the book say the answer is 2 then?
 
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Qube said:

Homework Statement



Integrate the definite integral ∫sin(x)dx given b = ∏ and a = 0.

Homework Equations



Fundamental theorem of calculus; definite integral = F(b) - F(a)

The Attempt at a Solution



The anti-derivative is -cos(x).

F(∏) = -(-1) = 1.
F(0) = 1.
F(b) - F(a) = 0.

Why does the book say the answer is 2 then?

Because F(0)=(-1) not 1.
 

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