- #1
wlooi
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Homework Statement
∫(sin x)√(1+cos2x) dx
Last edited:
wlooi said:Well, I got myself until:
[itex]\large - [/itex] [itex]\int \sqrt{1+y^2}[/itex] [itex]\large dy [/itex]
then I stucked again.
wlooi said:using 1+tan2v=sec2v , I got it until :
-∫sec3v dv
am I suppose to do by parts or is there other ways?
An integral of a function is a mathematical concept that calculates the area under a curve on a graph. It is represented by the symbol ∫ and has two limits, the lower and upper bound, which determine the range of the function that is being integrated.
The main purpose of finding the integral of a function is to determine the total value or quantity represented by that function. It is also used to find the rate of change of a function over a specific interval and to solve problems related to motion, area, and volume.
The integral of a function is calculated using a process called integration. There are two main types of integration: indefinite and definite. Indefinite integration involves finding a general antiderivative of a function, while definite integration involves finding the area under the curve of a function within specific limits.
The main difference between a definite and an indefinite integral is the presence of limits. Definite integrals have specific limits, while indefinite integrals do not. Additionally, definite integrals give a specific numerical value, while indefinite integrals give a general function as a solution.
The integral of a function is important in science because it allows us to model and analyze real-world phenomena. It is used in various fields such as physics, chemistry, and engineering to solve problems related to motion, growth, and change. It also helps us to understand the relationship between different variables in a system.