Question

Guide Questions:

1. How do you saive for the area of the shaded region in figure A?
2. How do you solve for the area of the shaded region in figure B?
3. Is method finding the shaded region in figure A and B the same? Why? or Why not?


please answer on 3 i need answers for that number 3 questions​

Answer 1

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

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;

`f(x) = e^(-t^2)`

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;

`A = \int\limits^1_0 {e^(-t^2)} \, dt = (1)/(2) \cdot √(\pi) * erf(t)`

Using a graphing calculator, we have;

`A = \int\limits^1_0 {e^(-t^2)} \, dt \approx 0.746824`

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.