14.01 Approximation of areas under a curve
Interactive practice questions
The graph below shows the function $f\left(x\right)=e^x$f(x)=ex.
Find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0≤x≤4 using the left-endpoint approximation and $4$4 rectangles.
Round your answer to three decimal places.
Find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0≤x≤4 using the right-endpoint approximation and $4$4 rectangles.
Round your answer to three decimal places.
Using technology, find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0≤x≤4 using the left-endpoint approximation and $50$50 rectangles.
Round your answer to four decimal places.
Use integration to find the exact area between the function and the $x$x-axis for $0\le x\le4$0≤x≤4.
Calculate the percentage error of the approximation in part (c) compared to the exact area.
Round your answer to the nearest percent.
The graph below shows the function $y=\sqrt{x+1}$y=√x+1.
The graph below shows the the function $f\left(x\right)=\cos x$f(x)=cosx.
The graph of $y=x^2-4$y=x2−4 is shown below.