Answer:
1. The area is found by using the formula for a rectangle
The area is 150 cm²
2. The area is found by the definite integral for the area between two points under a curve
3. The methods are different
The methods are different because the area of figure A is found by the multiplication between the dimensions, while the area of figure B is found by the difference between the values of the integral of the function between the points
Step-by-step explanation:
1. The area of the shaded figure A is found by multiplying the dimensions of the figure, which is the length multiplied by the breadth of the figure
From the question, we have;
The area of the rectangular figure, A = Length × Breadth
The length of the figure = 15 cm
The breadth of the rectangular figure = 10 cm
Therefore, we have;
A = 15 cm × 10 cm = 150 cm²
The area of the rectangular figure, A = 150 cm²
2. The bell shape of the figure B is obtained from a function f(x) as obtained from MIT mathematics website as follows;
[tex]f(x) = e^{-t^2}[/tex]
Therefore the area of the shaded region in the bell shaped figure between the points 0 and 1 on the x-axis is found by integration as follows;
[tex]A = \int\limits^1_0 {e^{-t^2}} \, dt = \dfrac{1}{2} \cdot \sqrt{\pi} \times erf(t)[/tex]
Using a graphing calculator, we have;
[tex]A = \int\limits^1_0 {e^{-t^2}} \, dt \approx 0.746824[/tex]
3. The method of finding the area of figure A is different from the method of finding the area of the figure B
The methods are different because the area of figure A is the area of the whole figure of a geometric shape with known formula for area while the area of of the shaded region has no predefined formula but is calculated using the calculus for the area under a curve.
