Login or Sign Up

Ask a New Question

Find the area under the curve given by y=coax from x=0 to x=pi/4 above the x-axis.

Draw a graph with an approximate rectangle (ie cut).
Calculate the area with an integral.

Area = ∫ cosx dx from 0 to π/4

= [sinx] from 0 to π/4
= sinπ/4 - sin0
= √2/2-0
= √2/2

Did you know?

Did you know that you can find the area under a curve by using integration? For example, if you have the equation y = co(ax) and want to find the area between the curve and the x-axis from x = 0 to x = π/4, you can follow these steps: 1. Start by sketching a graph representing the curve y = co(ax). 2. Divide the area between the curve and the x-axis into smaller rectangles. 3. Choose one of these rectangles, which will have a width of ∆x and a height equal to the corresponding y-value on the curve. 4. The area of this rectangle can be estimated by multiplying the width (∆x) by the height (y = co(ax)). 5. Repeat this process for all the rectangles until you have a good approximation of the total area. 6. To obtain an accurate measurement of the area, you can use integration. 7. Integrate the function y = co(ax) with respect to x from 0 to π/4, which will yield the exact area under the curve. By utilizing these calculations, you can accurately determine the area under a given curve and gain a better understanding of the relationship between mathematical functions and their graphical representations.