Find the area of the region bounded by the graphs of these equations

Question

(a) Use the rectangles in each graph to approximate the area of the region bounded by y = sin x, y = 0, x = 0 and x = pi.

(b) Describe how you could continue this process to obtain a more accurate approximation of the area.

Answer 1

Step 1:

(a)

The area of the region is bounded by , , and .

Area of the region is the sum of areas of the set of rectangles.

In the first case, the rectangle repeat at an interval of .

Area of the region using 4 rectangle in it is 1.8961.

In the second graph, the rectangle repeat at an interval of .

Area of the region using 6 rectangle inscribed in it is 1.954.

Step 2:

(b)

The area of the region could be more accurate when there are more number of rectangle.

More the number of rectangle, more accurate will be the area.

Solution :

(a) Area of the region using 4 rectangle in it is 1.8961.

     Area of the region using 6 rectangle inscribed in it is 1.954.

(b) The area of the region could be more accurate when there are more number of rectangle.