Miike012 said:I guess you can say that... The real question was ... estimate the area of cos(x) [0,pi/2] using 4 approximating rectangles and right endpoints..
That is easy so I wanted to try and solve for n rectangles..
LCKurtz said:I don't know of any nice formula for that sum. (That doesn't mean there isn't one.) Are you studying approximating sums for integrals but don't have the fundamental theorem of calculus yet?
Miike012 said:one more question...
Estimate the area under the graph of f(x) = 1 + x^2 from x = -1 to x = 2 using 6 rectangles and right end point.
Question:
Can I change the equation from 1 + x^2 to 1 + (x - 1)^2 and change the interval to x = 0 to x = 3 ??
This seems logical because technically it would be the same area.. and it is easier for me to break up into 6 rectangles.
To calculate the area under a trig graph, you need to use integration. The formula for finding the area under a curve is given by the integral of the function from the lower limit to the upper limit. For a trigonometric function, you would need to find the antiderivative and then evaluate the integral using the limits of integration.
The main difference between calculating the area under a trig graph and a regular graph is that trigonometric functions have a periodic nature. This means that the area under one cycle of the function may be different from the area under another cycle. Therefore, when calculating the area under a trig graph, you need to consider the appropriate limits of integration to get an accurate result.
Yes, you can use the same method of integration to calculate the area under any trig graph. However, the limits of integration may vary depending on the specific trig function and the interval over which you want to find the area. It is important to carefully choose the appropriate limits to get an accurate result.
Yes, the Riemann sum method can be used to approximate the area under a trig graph. However, since trigonometric functions are continuous, using a larger number of rectangles in the Riemann sum will result in a more accurate approximation of the area. It is recommended to use a computer or calculator to calculate the Riemann sum for a trig function with a large number of rectangles.
Calculating the area under a trig graph can be useful in various real-life applications such as physics, engineering, and economics. For example, in physics, the area under a velocity-time graph represents the displacement of an object, and the area under an acceleration-time graph represents the change in velocity. In engineering, the area under a force-displacement graph can represent the work done by a force, and in economics, the area under a demand or supply curve can represent the consumer surplus or producer surplus, respectively.