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Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = 1/2 using four approximationg rectangles and right
Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = 1/2 using four approximationg rectangles and right endpoints. Is your estimate an underestimate or an overestimate? Part 1 of 5 Rectangle areas are found by calculating height x width. The width of each rectangle equals Ax and the height of each rectangle is given by the function value at the right-hand side of the rectangle. So we must calculate R4 = _ ((x,)Ax = [f(x,) + f(x2) + f(x3) + f(x4)] Ax, Where X1, X2 X3, *4 represent the right-hand endpoints of four equal sub-intervals of 0, It. Since we wish to estimate the area over the interval |0, | using 4 rectangles of equal widths, then each rectangle will have width Ax = |00 1 7 Part 2 of 5 We wish to find R4 = [f( x ] ) + f( x 2 ) + f ( x3 ) + f( x4 )] ( ). Since X1, X2, X3 X4 represent the right-hand endpoints of the four sub-intervals of 0, -, then we must have the following. Exercise (b) Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = 1/2 using four approximationg rectangles and left endpoints. Is your estimate an underestimate or an overestimate? Part 1 of 5 We must calculate L4 = [ ((x ; _ 1 ) Ax = [f(x ) + f(x, ) + f(x2) + f(X3)]Ax, Where X X1, X2, *3 represent the left-hand endpoints of four equal sub-intervals of 0, I . Since we wish to estimate the area over the interval |0, |using 4 rectangles of equal widths, then each rectangle will have width Ax Part 2 of 5 We wish to find L4 = [f(x) + f( x, ) + f(x2 ) + f(x3)] ( ). Since X X1, X2, X3 represent the left-hand endpoints of the four sub-intervals of 0, , then we must have the following. X 3
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