First, watch the Youtube video to supplement your understanding of using integration to find the area under a curve. Jot down notes and questions you may have about the video. [br]Next, use the Geogebra template to test your understanding. Use the questions below to guide your work.
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Find the area under the curve from [math]x=1[/math] to [math]x=3[/math] using the curve [math]f\left(x\right)=x^2[/math] and the x axis. What is your answer? Then, use the sliders to check your work.
Find the area under the curve from [math]x=1[/math] to [math]x=3[/math] using the curve [math]f\left(x\right)=2x^2+1[/math] and the x-axis. What is your answer? How does the area compare to the area from the previous question? Use the sliders to check your work.
Find the area under the curve from [math]x=1[/math] to [math]x=4[/math] using the curve [math]f\left(x\right)=-3x^2+4[/math] and the x-axis. What is your answer? What are some differences between this question and the other questions? Use the sliders to check your work and the graph.
Go to the left side of the template, and change the degree of the polynomial (the highest power of x) from 2 to 3. Now, find the area under the curve from [math]x=0[/math] to [math]x=5[/math] using the curve [math]f\left(x\right)=-x^3+9[/math] and the x-axis. Check your work using the sliders.
How do you feel about this topic? 1 being "I cannot do any of these questions", 2 being "I can do these questions with help", 3 being "I can do these questions on my own". Select your answer below.