Quick one regarding Integration

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In summary, integration is a mathematical concept used to calculate the area under a curve and solve various problems in mathematics, physics, and engineering. It is important because it allows us to find exact values for difficult or impossible calculations and has practical applications in fields such as economics, biology, and statistics. There are two types of integration, definite and indefinite, and it is closely related to differentiation. Some real-world applications of integration include calculating volume, displacement, and average value, as well as in economics, physics, and biology.
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specwarop
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Gday,

Just a quick one regarding integration.
The rules at the back of my calculus book states that the Integral of
tan(u) du = In(|sec u|) + C

However, my calculators and Wolfram all give me the answer as being
tan(u) du = -In(|cos u|) + C

Which one is correct, which do I believe?

Regards
 
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  • #2
sec(u)= 1/cos(u) so ln(sec(u))= ln(1/cos(u))= -ln(cos(u)). They are exactly the same thing.

(And the natural logarithm is represented by ln ("ell en") not In ("eye en").)
 

FAQ: Quick one regarding Integration

What is integration?

Integration is a mathematical concept that involves calculating the area under a curve. It is used to solve a variety of problems in mathematics, physics, and engineering.

Why is integration important?

Integration is important because it allows us to find the exact value of quantities that would be difficult or impossible to calculate otherwise. It also has many practical applications in fields such as economics, biology, and statistics.

What are the two types of integration?

The two types of integration are definite and indefinite integration. Definite integration involves finding the exact area under a curve between two specific points, while indefinite integration involves finding a general antiderivative of a function.

How is integration related to differentiation?

Integration and differentiation are inverse operations. This means that the derivative of a function is the rate of change of the function, while the integral of a function is the function itself. They are closely related and often used together in solving mathematical problems.

What are some real-world applications of integration?

Integration has many real-world applications, such as calculating the volume of irregular shapes, finding the displacement of an object from its velocity function, and determining the average value of a function. It is also used in economics to calculate profit and loss, in physics to calculate work and energy, and in biology to model population growth.

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