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**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.