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Find the areas bounded by the indicated curves.$$y=2 x^{3}-x^{4}, y=0$$
$$A=\frac{8}{5}$$
Calculus 2 / BC
Chapter 26
Applications of Integration
Section 2
Areas by Integration
Missouri State University
Campbell University
University of Michigan - Ann Arbor
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I want to find the area bounded by the curves, Y equals two X cubed minus X to the fourth and Y equals zero. This question is challenging your understanding of how to find areas between curve which is an application of integration. So as such is not appropriate definitions we have at the area between two curves is for vertical components equal gonna go A to B, Y u minus one Z X. And before and all components A integral CBD X two minus X 20 Y. If we sketched curves out, we can identify the appropriate bounds as well as the curves integrate under so that we can solve this problem using these ones. So if we stretch this out we see that our polynomial is graft in our Y equals zero is represented by the X axis. Therefore the area that we sketch is highlighted in yellow. Thus we are all we need to do to to integrate this area is integrate two xq minus X to the fourth. From zero to its intercepts this gives half X to the fourth minus 1/5 extra from 0 to 2 equals eight bits
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