Question

Find the area of the region. Use a graphing utility to verify your result.

y = 2 sin(x) + sin(2x) the graph goes from x=0 to x=pi ...?

Answer 1

To find the area of the region represented by the equation y = 2 sin(x) + sin(2x) for x ranging from 0 to pi, we can use integration. The area of the region is 2.5 square units.

Step-by-step explanation:

To find the area of the region represented by the equation y = 2 sin(x) + sin(2x) for x ranging from 0 to pi, we can use integration. The formula to find the area under a curve is given by the definite integral of the function. In this case, we need to find the definite integral of the function y = 2 sin(x) + sin(2x) from x = 0 to x = pi.

By integrating the function, we get the following:

• The integral of 2 sin(x) is -2 cos(x)
• The integral of sin(2x) is -0.5 cos(2x)

Applying the limits from x = 0 to x = pi and calculating the difference between the two integrals gives us the area of the region as -2 cos(pi) - (-2 cos(0)) - 0.5 cos(2(pi)) - (-0.5 cos(2(0))). Simplifying further, the area of the region is 2 + 0.5 = 2.5 square units.