- #1
Jumpy Lee
- 20
- 0
Homework Statement
[tex]\int sin^3(x)cos^2(x)dx[/tex]
The Attempt at a Solution
[tex]\int sin^3x(1-sin^2x)dx =[/tex] [tex]\int sin^3x- sin^5xdx[/tex]
i get stuck here what do i do next and is this even right
Jumpy Lee said:Homework Statement
[tex]\int sin^3(x)cos^2(x)dx[/tex]
The Attempt at a Solution
[tex]\int sin^3x(1-sin^2x)dx =[/tex] [tex]\int sin^3x- sin^5xdx[/tex]
i get stuck here what do i do next and is this even right
An integral is a mathematical tool used to calculate the area under a curve. It is represented by the symbol ∫ and is used to find the total value of a function over a given interval.
To evaluate an integral, you must first determine the limits of integration, which are the starting and ending points for the interval. Then, you use integration techniques, such as substitution or integration by parts, to solve for the value of the integral.
A definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral will result in a single numerical value, while an indefinite integral will result in a function with a constant of integration.
Evaluating integrals is important in science because it allows us to calculate important values, such as area, volume, and probability, which are essential in many scientific fields. Integrals also help us understand the behavior of functions and solve problems in physics, chemistry, and engineering.
Yes, there are many applications of integrals in real life, such as calculating the volume of a shape, finding the average value of a function, and determining the work done by a force. Integrals are also used in fields like economics, biology, and medicine to analyze data and make predictions.