`y = sin(x), 0<=x<=pi` Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

Textbook Question

Chapter 5, 5.3 - Problem 51 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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Refer the graph in the attached image.

From the graph it appears that the area is `~~` 2/3 of the rectangle.

Area of the region= `~~` 2/3(Area of rectangle) 

Area of the region =`~~2/3(pi*1)=2/3*3.14=2.09` 

Actual Area of the region=`int_0^pisin(x)dx`

`=[-cos(x)]_0^pi`

`=[-cos(pi)]-[-cos(0)]`

`=-cos(pi)+cos(0)`

`=-(-1)+1`

=2

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