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 = sinx and the x-axis between x = 0 and x = 22/7, we can use definite integration.
First, let's graph the curve y = sinx between the given limits:
If we sketch the graph of y = sinx, we can see that it is a periodic function that oscillates between -1 and 1. Specifically, between the values of x = 0 and x = 2π (which is approximately 22/7), the graph covers one full period of the sine function.
To find the area between the curve and the x-axis, we need to calculate the definite integral of y = sinx with respect to x, between x = 0 and x = 22/7.
The definite integral of sinx with respect to x can be written as:
∫[0, 22/7] sinx dx
To find this integral, we can use basic integral rules and evaluate it. The integral of sinx is -cosx, so we have:
= [-cosx] from x = 0 to x = 22/7
= -cos(22/7) - (-cos(0))
= -cos(22/7) - (-1)
= -cos(22/7) + 1
To find the numerical value of this expression, we can use a calculator to evaluate -cos(22/7) and then subtract it from 1.
So, the area enclosed by the curve y = sinx and the x-axis between x = 0 and x = 22/7 is approximately equal to 2.