Find the area enclosed by the curve y=sinx and the x-axis between x=0 and x=22/7
To find the area enclosed by the curve y = sin(x) and the x-axis between x = 0 and x = 22/7, we can use integration.
First, let's represent the given curve, y = sin(x), and the x-axis in a graph to visualize the area we want to find.
The integral of a function gives us the area under the curve between two points. In this case, we want to find the area above the x-axis, so the integral will be positive.
To find the area between two specific x-values, we need to compute the definite integral over that interval. In this case, we want the area between x = 0 and x = 22/7, so we will integrate the function y = sin(x) with respect to x from 0 to 22/7.
∫[0, 22/7] sin(x) dx
To perform this integration, we can use any suitable integration technique, such as the power rule or substitution rule. However, the integral of sin(x) is a well-known result:
∫ sin(x) dx = -cos(x)
Applying the indefinite integral and evaluating it between x = 0 and x = 22/7:
[-cos(x)] [0, 22/7]
Substituting the values:
[-cos(22/7)] - [-cos(0)]
Since cos(0) = 1, the expression simplifies to:
-cos(22/7) - (-1)
Finally, we calculate the value of the expression:
Approximately, the area enclosed by the given curve and the x-axis between x = 0 and x = 22/7 is 0.288.