- #1
s883
- 5
- 0
Homework Statement
π/2
d x/
∫ (x2 - 2x cosx + 1)
0
п
∫ sin x. ex^2dx
-п
A definite integral is a mathematical concept that represents the area under a curve between two points on the x-axis. It is used to calculate the total change of a function over a specific interval.
To solve a definite integral, you need to first evaluate the integral by finding the antiderivative of the function, then plug in the upper and lower limits of integration and subtract the results. This will give you the numerical value of the integral.
The upper limit of integration is listed first in a definite integral because it represents the end point of the interval. This follows the convention of reading from left to right and makes the integral easier to understand and evaluate.
Yes, the definite integral is specifically designed to find the area under a curve. By evaluating the definite integral between two points on the x-axis, you can calculate the area of the region between the curve and the x-axis.
The limits of integration represent the starting and ending points of the interval over which you are calculating the definite integral. In this case, the interval is from π/2 to 0, meaning you are finding the area under the curve between the points π/2 and 0 on the x-axis.