Find the area between the curves \(y = x\) and \(y = x^2\)
Compute the area between \(y = \sin{x}\) and \(y = \cos{x}\) and the interval \([\frac{\pi}{4}, \frac{5\pi}{4}]\)
Find the average value on \([0, 16]\) of \(f(x) = \sqrt{x}\)
What is the average value of the function \(f(x) = 3x^2 - 2x\) on \([1, 4]\)
Determine the volume of the solid generated by rotating the function about the x-axis on \([0,3]\)\(y = \sqrt{9 - x^2}\)
Find the average value of the function \(h(x) = \cos^4{(x)}\sin(x)\) on \([0, \pi]\)
Determine the volume of the solid generated by rotating the function about the y-axis on \([0,4]\) \(y = \sqrt{x}\)
Use the shell method to determine the volume formed by the bounded region rotated about the x-axis.\(y = x^2\), \(y = 0\), \(x = 2\)
Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.\(y = x^2 + 2\)\(y = 0\), \(x = 0\), \(x = 2\)
Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis\(y = 2x^2\), \(y = 0\), \(x = 2\)
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