baquid said:Homework Statement
Sketch the region in the first quadrant enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=4cosx, y=6sin2x, x=0.
Homework Equations
The Attempt at a Solution
I got the intersections, which are x=pi/2, arcsin1/3 as well as x=0 but I seem to keep getting 10/3, which is not the right answer.
The integral question of areas between curves is a mathematical concept in which the area between two curves is calculated using integration techniques. It is an important concept in calculus and is used to solve various real-world problems.
To find the area between two curves, you need to first find the points of intersection of the two curves. Then, you can use integration to find the area between these points. The integral of the function that represents the difference between the two curves will give you the desired area.
The concept of integral question: areas between curves is used to solve various real-life problems, such as determining the volume of irregular shapes, finding the area under a curve for statistical analysis, and calculating work done in physics. It also has applications in engineering, finance, and economics.
There are two main methods used to solve integral question: areas between curves - the Riemann sum method and the Trapezoid rule method. The Riemann sum method involves dividing the area into smaller rectangles and calculating their individual areas, while the Trapezoid rule method approximates the area using trapezoids.
One common mistake to avoid is forgetting to include the negative sign when integrating the function representing the difference between the two curves. Another mistake is not properly identifying the points of intersection of the curves, which can lead to incorrect results. It is also important to carefully choose the limits of integration to get an accurate result.