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Standard Level

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.

Loading Graph...

a

Find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0x4 using the left-endpoint approximation and $4$4 rectangles.

Round your answer to three decimal places.

b

Find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0x4 using the right-endpoint approximation and $4$4 rectangles.

Round your answer to three decimal places.

c

Using technology, find an estimate for the area between the function and the $x$x-axis for $0\le x\le4$0x4 using the left-endpoint approximation and $50$50 rectangles.

Round your answer to four decimal places.

d

Use integration to find the exact area between the function and the $x$x-axis for $0\le x\le4$0x4.

e

Calculate the percentage error of the approximation in part (c) compared to the exact area.

Round your answer to the nearest percent.

Medium
5min

The graph below shows the function $y=\sqrt{x+1}$y=x+1.

Medium
5min

The graph below shows the the function $f\left(x\right)=\cos x$f(x)=cosx.

Hard
5min

The graph of $y=x^2-4$y=x24 is shown below.

Easy
6min
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