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 need to calculate the definite integral of the function over that interval.
Step 1: Start with the definite integral formula: ∫[a, b] f(x) dx, where a = 0 and b = 22/7.
Step 2: In this case, the function f(x) is y = sin(x).
Step 3: Rewrite the given equation in terms of x: y = sin(x).
Step 4: Plug in the function: ∫[0, 22/7] sin(x) dx.
Step 5: Evaluate the integral using the trigonometric identity: ∫ sin(x) dx = -cos(x) + C.
Step 6: Apply the limits of integration: [-cos(x)] evaluated from 0 to 22/7.
Step 7: Substitute the upper limit: -cos(22/7).
Step 8: Subtract the value at the lower limit: -cos(0).
Step 9: Simplify: -cos(22/7) + cos(0).
Step 10: The final result is the area enclosed by the curve and the x-axis between x = 0 and x = 22/7, which is -cos(22/7) + 1 square units.