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Form 4 Mathematics area and approximation:Trapezoidal rule questions and answers
Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below.
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1.
The travel graph of a cyclist given below represents a journey from 9 am up to 11 am. By dividing the shaded region into six strips of equal width and using trapezium rule, estimate the total distance travelled.
2.
In order to sketch the cross-section of a ditch 175 cm wide, the depth of water was measured at intervals of 25 cm from one of the banks. The readings of the depths were as follows; (i) Sketch the cross-section of the ditch. (ii) Use trapezoidal rule to estimate the area of the cross-section.
3.
(a) Use the trapezoidal rule to find the area under the curve #y=x^2 + 1# from x=1 to x=15 using seven strips. (b) The cross-sectional area in #m^2# along the length of an 18 m wooden log are: 5.0, 5.4, 7.0, 8.0, 5.5, 5.8, 6.0 The cross-sectional areas are equally spaced. The first and the last areas represent the ends of the log. Estimate its volume using the trapezoidal rule.
4.
Complete the table below for the function #y=3x^2 – 8x + 10#. Using the values in the table and the trapezoidal rule, estimate the area bounded by the curve #y=3x^2 – 8x + 10# and the lines y=0, x=0 and x=10.
5.
Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below.
6.
The graph below consists of a non-quadratic part (#0 lex lt 2#) and a quadratic part (#2 le x le8#). The quadratic part is #y=x^2 – 3x + 5#, #2 lt x lt8#. (a) Complete the table beside: (b) Use the trapezoidal rule with six strips to estimate the area enclosed by the curve, X-axis and the line x=2 and x=8
7.
A particle is projected from the origin. Its speed was recorded as shown in the table below. Use trapezoidal rule to estimate the distance covered by the particle within the 35 seconds.
8.
The table below shows values of x and the corresponding values of y for a given curve. (a) Use the trapezium rule with seven ordinates and the values in the table in the table only to estimate the area enclosed by the curve, x axis and the line x= #pi# 2 to four decimal places. (take #pi#=3.142) (b) The exact value of the area enclosed by the curve is known to be 0.8940.
9.
A circle center O has the equation #x^2 + y^2 =4#. The area of the circle in the first quadrant is divided into 5 vertical strips each of width 0.4 cm. (a) Use the equation of the circle to complete the table below for values of y correct to 2 decimal places. (b) Use the trapezium rule to estimate the area of the circle.
10.
(a) Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve #y=-x^2 + 6x + 1#, the lines x=0, y=0 and x=6. (b) Calculate : (i) The area of the region in (a) above by integration. (ii) The percentage error of the estimated area to the actual area of the region, correct to two decimal places.
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