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C2 INTEGRATION Answers - Worksheet A page 2 ... total area = 8 3 + 5 12 = 1 12 3 shaded area = 6 ...
Integration can be used to calculate areas. In simple cases, the area is given by a single definite integral. But sometimes the integral gives a negative answer which is minus the area, and in more complicated cases the correct answer can be obtained only by splitting the area into several parts and adding or subtracting the appropriate integrals.
C2 INTEGRATION Answers - Worksheet A page 2 ... total area = 8 3 + 5 12 = 1 12 3 shaded area = 6 ...
There are two ways to solve this problem: we can calculate the area between two functions and using the vertical elements and integrate with respect to x, or we can use the horizontal elements and calculate the area between the y -axis and the function integrating the functions with respect to y.
Use calculus to find the total area of the finite region, shown shaded in the diagram, that is between
(a) Find the x-coordinate at the point A and the x-coordinate at the point B. (3) The region R, as shown shaded in the diagram above, is enclosed by the loop of the curve. (b) Use integration to find the area of R. (6) Total 9 marks) R bounded by the x-axis, the y-axis and the curve. with equation y = 3 cos . , 0 ≤ x ≤ 3 π . 3 2.
Use your expression in a and integration to find an estimate for the area of R. Use the trapezium rule with 6 equally-spaced ordinates to find another estimate for the area of R. 8= x2 + 16xR4 xThe diagram shows the curve. = x2 + 16 for x > 0.Show that the stationary point on the curve.
