### Week 14: Integration by Tables. Area under a curve and between curves

The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive. The area between two functions is equal to the area of the function located above minus the area of the function that lies below. 1. Calculate the area of the space enclosed by the parabola y = x² + 2 and the straight line that passes through the points A(−1, 0) and B(1, 4). Area is calculated by multiplying the length of a shape by its width. In this case, we could work out the area of this rectangle even if it wasn't on squared paper, just by working out 5cm x 5cm = 25cm² (the shape is not drawn to scale). The area under a curve between two points is found out by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be calculated using integration with given limits.